NCERT Class 12 Mathematics Solutions
Chapter 7: Integrals
The topics and sub-topics included in the Integrals chapter are the following:
Section Name | Topic Name |
7 | Integrals |
Question 1 (7)
1 | Introduction |
7.2 | Integration as an Inverse Process of Differentiation |
7.3 | Methods of Integration |
7.4 | Integrals of some Particular Functions |
7.5 | Integration by Partial Fractions |
7.6 | Integration by Parts |
7.7 | Definite Integral |
7.8 | Fundamental Theorem of Calculus |
7.9 | Evaluation of Definite Integrals by Substitution |
7.10 | Some Properties of Definite Integrals |
- Integration Formulas
- Integrals Class 12 Ex 7.1
- Integrals Class 12 Ex 7.1 in Hindi Medium
- Integrals Class 12 Ex 7.2
- Integrals Class 12 Ex 7.2 in Hindi Medium
- Integrals Class 12 Ex 7.3
- Integrals Class 12 Ex 7.3 in Hindi Medium
- Integrals Class 12 Ex 7.4
- Integrals Class 12 Ex 7.4 in Hindi Medium
- Integrals Class 12 Ex 7.5
- Integrals Class 12 Ex 7.5 in Hindi Medium
- Integrals Class 12 Ex 7.6
- Integrals Class 12 Ex 7.6 in Hindi Medium
- Integrals Class 12 Ex 7.7
- Integrals Class 12 Ex 7.7 in Hindi Medium
- Integrals Class 12 Ex 7.8
- Integrals Class 12 Ex 7.8 in Hindi Medium
- Integrals Class 12 Ex 7.9
- Integrals Class 12 Ex 7.9 in Hindi Medium
- Integrals Class 12 Ex 7.10
- Integrals Class 12 Ex 7.10 in Hindi Medium
- Integrals Class 12 Ex 7.11
- Integrals Class 12 Ex 7.11 in Hindi Medium
- Integrals Class 12 Miscellaneous Exercise
- RD Sharma Class 12 Integrals
- NCERT Exemplar Class 12 Maths Integrals
- Integrals Class 12 Notes Maths Chapter 7
- Important Questions Class 12 Maths Integrals
- JEE Main Mathematics Definite and Indefinite Integrals
Class 12 Maths Chapter 7 NCERT Solutions Integrals
- Introduction
- Integration as an Inverse Process of Differentiation
- Geometrical interpretation of indefinite integral
- Some properties of indefinite integral
- Comparison between differentiation and integration
- Methods of Integration
- Integration by substitution
- Integration using trigonometric identities
- Integrals of Some Particular Functions
- Integration by Partial Fractions
- Integration by Parts
- Integral of the type
- Integrals of some more types
- Definite Integral
- Definite integral as the limit of a sum
- Fundamental Theorem of Calculus
- Area function
- First fundamental theorem of integral calculus
- Second fundamental theorem of integral calculus
- Evaluation of Definite Integrals by Substitution
- Some Properties of Definite Integrals
Integrals Ex 7.1 Class 12
Ex 7.1 Class 12 Maths Question 1.
sin 2x
Ex 7.1 Class 12 Maths Question 2.
cos 3x
Solution:
Ex 7.1 Class 12 Maths Question 3.
Solution:
Ex 7.1 Class 12 Maths Question 4.
(ax + c)²
Solution:
Ex 7.1 Class 12 Maths Question 5.
Ex 7.1 Class 12 Maths Solution:
Find the following integrals in Exercises 6 to 20 :
Ex 7.1 Class 12 Maths Question 6.
Solution:
Ex 7.1 Class 12 Maths Question 7.
Solution:
Ex 7.1 Class 12 Maths Question 8.
Solution:
Ex 7.1 Class 12 Maths Question 9.
Solution:
Ex 7.1 Class 12 Maths Question 10.
Solution:
Ex 7.1 Class 12 Maths Question 11.
Solution:
Ex 7.1 Class 12 Maths Question 12.
Solution:
Ex 7.1 Class 12 Maths Question 13.
Solution:
Ex 7.1 Class 12 Maths Question 14.
Solution:
Ex 7.1 Class 12 Maths Question 15.
Solution:
Ex 7.1 Class 12 Maths Question 16.
Solution:
Ex 7.1 Class 12 Maths Question 17.
Solution:
Ex 7.1 Class 12 Maths Question 18.
Solution:
Ex 7.1 Class 12 Maths Question 19.
Solution:
Ex 7.1 Class 12 Maths Question 20.
Solution:
Choose the correct answer in Exercises 21 and 22.
Ex 7.1 Class 12 Maths Question 21.
The antiderivative equals
(a)
(b)
(c)
(d)
Solution:
Ex 7.1 Class 12 Maths Question 22.
If such that f(2)=0 then f(x) is
(a)
(b)
(c)
(d)
Solution:
Move to Top →Class 12 Integrals Chapter 7
Integrals Ex 7.2 Class 12
Integrate the functions in Exercises 1 to 37:
Ex 7.2 Class 12 Maths Question 1.
Solution:
Ex 7.2 Class 12 Maths Question 2.
Solution:
Ex 7.2 Class 12 Maths Question 3.
Solution:
Ex 7.2 Class 12 Maths Question 4.
sinx sin(cosx)
Solution:
Ex 7.2 Class 12 Maths Question 5.
sin(ax+b) cos(ax+b)
Solution:
Ex 7.2 Class 12 Maths Question 6.
Solution:
Ex 7.2 Class 12 Maths Question 7.
Solution:
Ex 7.2 Class 12 Maths Question 8.
Solution:
Ex 7.2 Class 12 Maths Question 9.
Solution:
Ex 7.2 Class 12 Maths Question 10.
Solution:
Ex 7.2 Class 12 Maths Question 11.
Solution:
Ex 7.2 Class 12 Maths Question 12.
Solution:
Ex 7.2 Class 12 Maths Question 13.
Solution:
Ex 7.2 Class 12 Maths Question 14.
Solution:
Ex 7.2 Class 12 Maths Question 15.
Solution:
Ex 7.2 Class 12 Maths Question 16.
Solution:
Ex 7.2 Class 12 Maths Question 17.
Solution:
Ex 7.2 Class 12 Maths Question 18.
Solution:
Ex 7.2 Class 12 Maths Question 19.
Solution:
Ex 7.2 Class 12 Maths Question 20.
Solution:
Ex 7.2 Class 12 Maths Question 21.
tan²(2x-3)
Solution:
∫tan²(2x-3)dx = ∫[sec²(2x-3)-1]dx = I
put 2x-3 = t
so that 2dx = dt
I = ∫sec²t dt-x+c
=
=
Ex 7.2 Class 12 Maths Question 22.
sec²(7-4x)
Solution:
Ex 7.2 Class 12 Maths Question 23.
Solution:
Ex 7.2 Class 12 Maths Question 24.
Solution:
Ex 7.2 Class 12 Maths Question 25.
Solution:
Ex 7.2 Class 12 Maths Question 26.
Solution:
Ex 7.2 Class 12 Maths Question 27.
Solution:
Ex 7.2 Class 12 Maths Question 28.
Solution:
Ex 7.2 Class 12 Maths Question 29.
cotx log sinx
Solution:
Ex 7.2 Class 12 Maths Question 30.
Solution:
Ex 7.2 Class 12 Maths Question 31.
Solution:
Ex 7.2 Class 12 Maths Question 32.
Solution:
Ex 7.2 Class 12 Maths Question 33.
Solution:
Ex 7.2 Class 12 Maths Question 34.
Solution:
Ex 7.2 Class 12 Maths Question 35.
Solution:
Ex 7.2 Class 12 Maths Question 36.
Solution:
Ex 7.2 Class 12 Maths Question 37.
Solution:
Choose the correct answer in exercises 38 and 39
Ex 7.2 Class 12 Maths Question 38.
(a) 10x – x10 + C
(b) 10x + x10 + C
(c) (10x – x10) + C
(d) log (10x + x10) + C
Solution:
Ex 7.2 Class 12 Maths Question 39.
(a) tanx + cotx + c
(b) tanx – cotx + c
(c) tanx cotx + c
(d) tanx – cot2x + c
Solution:
Move to Top →Class 12 Integrals Chapter 7
Integrals Ex 7.3 Class 12
Find the integrals of the functions in Exercises 1 to 22.
Ex 7.3 Class 12 Maths Question 1.
sin²(2x+5)
Solution:
Ex 7.3 Class 12 Maths Question 2.
sin3x cos4x
Solution:
Ex 7.3 Class 12 Maths Question 3.
∫cos2x cos4x cos6x dx
Solution:
Ex 7.3 Class 12 Maths Question 4.
∫sin3(2x+1)dx
Solution:
Ex 7.3 Class 12 Maths Question 5.
sin3x cos3x
Solution:
Ex 7.3 Class 12 Maths Question 6.
sinx sin2x sin3x
Solution:
Ex 7.3 Class 12 Maths Question 7.
sin 4x sin 8x
Solution:
Ex 7.3 Class 12 Maths Question 8.
Solution:
Ex 7.3 Class 12 Maths Question 9.
Solution:
Ex 7.3 Class 12 Maths Question 10.
∫sinx4dx
Solution:
Ex 7.3 Class 12 Maths Question 11.
cos42x
Solution:
Ex 7.3 Class 12 Maths Question 12.
Solution:
Ex 7.3 Class 12 Maths Question 13.
Solution:
Ex 7.3 Class 12 Maths Question 14.
Solution:
Ex 7.3 Class 12 Maths Question 15.
Solution:
Ex 7.3 Class 12 Maths Question 16.
tan4x
Solution:
Ex 7.3 Class 12 Maths Question 17.
Solution:
Ex 7.3 Class 12 Maths Question 18.
Solution:
Ex 7.3 Class 12 Maths Question 19.
Solution:
Ex 7.3 Class 12 Maths Question 20.
Solution:
Ex 7.3 Class 12 Maths Question 21.
sin-1(cos x)
Solution:
Ex 7.3 Class 12 Maths Question 22.
Solution:
Ex 7.3 Class 12 Maths Question 23.
(a) tanx+cotx+c
(b) tanx+cosecx+c
(c) -tanx+cotx+c
(d) tanx+secx+c
Solution:
Ex 7.3 Class 12 Maths Question 24.
(a) -cot(e.xx)+c
(b) tan(xex)+c
(c) tan(ex)+c
(d) cot ex+c
Solution:
Move to Top →Class 12 Integrals Chapter 7
Integrals Class 12 Ex 7.4
Ex 7.4 Class 12 Maths Question 1.
Solution:
Ex 7.4 Class 12 Maths Question 2.
Solution:
Ex 7.4 Class 12 Maths Question 3.
Solution:
Ex 7.4 Class 12 Maths Question 4.
Solution:
Ex 7.4 Class 12 Maths Question 5.
Solution:
Ex 7.4 Class 12 Maths Question 6.
Solution:
Ex 7.4 Class 12 Maths Question 7.
Solution:
Ex 7.4 Class 12 Maths Question 8.
Solution:
Ex 7.4 Class 12 Maths Question 9.
Solution:
Ex 7.4 Class 12 Maths Question 10.
Solution:
Ex 7.4 Class 12 Maths Question 11.
Solution:
Ex 7.4 Class 12 Maths Question 12.
Solution:
Ex 7.4 Class 12 Maths Question 13.
Solution:
Ex 7.4 Class 12 Maths Question 14.
Solution:
Ex 7.4 Class 12 Maths Question 15.
Solution:
Ex 7.4 Class 12 Maths Question 16.
Solution:
Ex 7.4 Class 12 Maths Question 17.
Solution:
Ex 7.4 Class 12 Maths Question 18.
Solution:
put 5x-2=A(1+2x+3x²)+B
⇒ 6A=5, A=, B=
Ex 7.4 Class 12 Maths Question 19.
Solution:
Ex 7.4 Class 12 Maths Question 20.
Solution:
Ex 7.4 Class 12 Maths Question 21.
Solution:
Ex 7.4 Class 12 Maths Question 22.
Solution:
Ex 7.4 Class 12 Maths Question 23.
Solution:
Ex 7.4 Class 12 Maths Question 24.
(a) xtan-1(x+1)+c
(b) (x+1)tan-1x+c
(c) tan-1(x+1)+c
(d) tan-1x+c
Solution:
Ex 7.4 Class 12 Maths Question 25.
(a)
(b)
(c)
(d)
Solution:
Move to Top →Class 12 Integrals Chapter 7
Integrals Class 12 Ex 7.5
Ex 7.5 Class 12 Maths Question 1.
Solution:
Ex 7.5 Class 12 Maths Question 2.
Solution:
Ex 7.5 Class 12 Maths Question 3.
Solution:
Ex 7.5 Class 12 Maths Question 4.
Solution:
Ex 7.5 Class 12 Maths Question 5.
Solution:
Ex 7.5 Class 12 Maths Question 6.
Solution:
Ex 7.5 Class 12 Maths Question 7.
Solution:
Ex 7.5 Class 12 Maths Question 8.
Solution:
Ex 7.5 Class 12 Maths Question 9.
Solution:
Ex 7.5 Class 12 Maths Question 10.
Solution:
Ex 7.5 Class 12 Maths Question 11.
Solution:
Ex 7.5 Class 12 Maths Question 12.
Solution:
Ex 7.5 Class 12 Maths Question 13.
Solution:
Ex 7.5 Class 12 Maths Question 14.
Solution:
Ex 7.5 Class 12 Maths Question 15.
Solution:
Ex 7.5 Class 12 Maths Question 16.
[Hint : multiply numerator and denominator by xn-1and put xn= t ]
Solution:
Ex 7.5 Class 12 Maths Question 17.
Solution:
Ex 7.5 Class 12 Maths Question 18.
Solution:
Ex 7.5 Class 12 Maths Question 19.
Solution:
Ex 7.5 Class 12 Maths Question 20.
Solution:
Ex 7.5 Class 12 Maths Question 21.
Solution:
Ex 7.5 Class 12 Maths Question 22.
choose the correct answer in each of the following :
(a)
(b)
(c)
(d) log|(x-1)(x-2)|+c
Solution:
Ex 7.5 Class 12 Maths Question 23.
(a)
(b)
(c)
(d)
Solution:
Move to Top →Class 12 Integrals Chapter 7
Integrals Class 12 Ex 7.6
Ex 7.6 Class 12 Maths Question 1.
x sinx
Solution:
Ex 7.6 Class 12 Maths Question 2.
x sin3x
Solution:
Ex 7.6 Class 12 Maths Question 3.
Solution:
Ex 7.6 Class 12 Maths Question 4.
x logx
Solution:
Ex 7.6 Class 12 Maths Question 5.
x log2x
Solution:
Ex 7.6 Class 12 Maths Question 6.
Solution:
Ex 7.6 Class 12 Maths Question 7.
Solution:
Ex 7.6 Class 12 Maths Question 8.
Solution:
Ex 7.6 Class 12 Maths Question 9.
Solution:
Ex 7.6 Class 12 Maths Question 10.
Solution:
Ex 7.6 Class 12 Maths Question 11.
Solution:
Ex 7.6 Class 12 Maths Question 12.
x sec²x
Solution:
Ex 7.6 Class 12 Maths Question 13.
Solution:
Ex 7.6 Class 12 Maths Question 14.
x(logx)²
Solution:
Ex 7.6 Class 12 Maths Question 15.
(x²+1)logx
Solution:
Ex 7.6 Class 12 Maths Question 16.
Solution:
Ex 7.6 Class 12 Maths Question 17.
Solution:
Ex 7.6 Class 12 Maths Question 18.
Solution:
Ex 7.6 Class 12 Maths Question 19.
Solution:
Ex 7.6 Class 12 Maths Question 20.
Solution:
Ex 7.6 Class 12 Maths Question 21.
Solution:
Ex 7.6 Class 12 Maths Question 22.
Solution:
Choose the correct answer in exercise 23 and 24
Ex 7.6 Class 12 Maths Question 23.
(a)
(b)
(c)
(d)
Solution:
Ex 7.6 Class 12 Maths Question 24.
(a)
(b)
(c)
(d)
Solution:
Move to Top →Class 12 Integrals Chapter 7
Class 12 Integrals Ex 7.7
Integral the function in exercises 1 to 9
Ex 7.7 Class 12 Maths Question 1.
Solution:
Ex 7.7 Class 12 Maths Question 2.
Solution:
Ex 7.7 Class 12 Maths Question 3.
Solution:
Ex 7.7 Class 12 Maths Question 4.
Solution:
Ex 7.7 Class 12 Maths Question 5.
Solution:
Ex 7.7 Class 12 Maths Question 6.
Solution:
Ex 7.7 Class 12 Maths Question 7.
Solution:
Ex 7.7 Class 12 Maths Question 8.
Solution:
Ex 7.7 Class 12 Maths Question 9.
Solution:
Choose the correct answer in the Exercises 10 to 11:
Ex 7.7 Class 12 Maths Question 10.
(a)
(b)
(c)
(d)
Solution:
Ex 7.7 Class 12 Maths Question 11.
Solution:
Move to Top →Class 12 Integrals Chapter 7
Class 12 Integrals Ex 7.8
Ex 7.8 Class 12 Maths Question 1.
Solution:
Ex 7.8 Class 12 Maths Question 2.
Solution:
Ex 7.8 Class 12 Maths Question 3.
Solution:
Ex 7.8 Class 12 Maths Question 4.
Solution:
Ex 7.8 Class 12 Maths Question 5.
Solution:
Ex 7.8 Class 12 Maths Question 6.
Solution:
Move to Top →Class 12 Integrals Chapter 7
Class 12 Integrals Ex 7.9
Ex 7.9 Class 12 Maths Question 1.
Solution:
Ex 7.9 Class 12 Maths Question 2.
Solution:
Ex 7.9 Class 12 Maths Question 3.
Solution:
Ex 7.9 Class 12 Maths Question 4.
Solution:
Ex 7.9 Class 12 Maths Question 5.
Solution:
Ex 7.9 Class 12 Maths Question 6.
Solution:
Ex 7.9 Class 12 Maths Question 7.
Solution:
Ex 7.9 Class 12 Maths Question 8.
Solution:
Ex 7.9 Class 12 Maths Question 9.
Solution:
Ex 7.9 Class 12 Maths Question 10.
Solution:
Ex 7.9 Class 12 Maths Question 11.
Solution:
Ex 7.9 Class 12 Maths Question 12.
Solution:
Ex 7.9 Class 12 Maths Question 13.
Solution:
Ex 7.9 Class 12 Maths Question 14.
Solution:
Ex 7.9 Class 12 Maths Question 15.
Solution:
Ex 7.9 Class 12 Maths Question 16.
Solution:
Ex 7.9 Class 12 Maths Question 17.
Solution:
Ex 7.9 Class 12 Maths Question 18.
Solution:
Ex 7.9 Class 12 Maths Question 19.
Solution:
Ex 7.9 Class 12 Maths Question 20.
Solution:
Ex 7.9 Class 12 Maths Question 21.
(a)
(b)
(c)
(d)
Solution:
Ex 7.9 Class 12 Maths Question 22.
(a)
(b)
(c)
(d)
Solution:
Move to Top →Class 12 Integrals Chapter 7
Integration Class 12 Ex 7.10
Ex 7.10 Class 12 Maths Question 1:
Solution:
Ex 7.10 Class 12 Maths Question 2:
Solution:
Ex 7.10 Class 12 Maths Question 3:
Solution:
Ex 7.10 Class 12 Maths Question 4:
Solution:
Ex 7.10 Class 12 Maths Question 5:
Solution:
Ex 7.10 Class 12 Maths Question 6:
Solution:
Ex 7.10 Class 12 Maths Question 7:
Solution:
Ex 7.10 Class 12 Maths Question 8:
Solution:
Ex 7.10 Class 12 Maths Question 9:
Solution:
Ex 7.10 Class 12 Maths Question 10:
Solution:
Ex 7.10 Class 12 Maths Question 11:
Solution:
Ex 7.10 Class 12 Maths Question 12:
Solution:
Ex 7.10 Class 12 Maths Question 13:
Solution:
Ex 7.10 Class 12 Maths Question 14:
Solution:
Ex 7.10 Class 12 Maths Question 15:
Solution:
Ex 7.10 Class 12 Maths Question 16:
Solution:
Ex 7.10 Class 12 Maths Question 17:
Solution:
Ex 7.10 Class 12 Maths Question 18:
Solution:
Ex 7.10 Class 12 Maths Question 19:
Solution:
Ex 7.10 Class 12 Maths Question 20:
Solution:
Move to Top →Class 12 Integrals Chapter 7
Move to Top →Class 12 Integrals Chapter 7
Miscellaneous Exercise Class 11 Maths Question 1:
Solution:
Miscellaneous Exercise Class 11 Maths Question 2:
Solution:
Miscellaneous Exercise Class 11 Maths Question 3:
Solution:
vMiscellaneous Exercise Class 11 Maths Question 4:
Solution:
Miscellaneous Exercise Class 11 Maths Question 5:
Solution:
Miscellaneous Exercise Class 11 Maths Question 6:
Solution:
Miscellaneous Exercise Class 11 Maths Question 7:
Solution:
Miscellaneous Exercise Class 11 Maths Question 8:
Solution:
Miscellaneous Exercise Class 11 Maths Question 9:
Solution:
Miscellaneous Exercise Class 11 Maths Question 10:
Solution:
Miscellaneous Exercise Class 11 Maths Question 11:
Solution:
Miscellaneous Exercise Class 11 Maths Question 12:
Solution:
Miscellaneous Exercise Class 11 Maths Question 13:
Solution:
Miscellaneous Exercise Class 11 Maths Question 14:
Solution:
Miscellaneous Exercise Class 11 Maths Question 15:
Solution:
Miscellaneous Exercise Class 11 Maths Question 16:
Solution:
Miscellaneous Exercise Class 11 Maths Question 17:
Solution:
Miscellaneous Exercise Class 11 Maths Question 18:
Solution:
Miscellaneous Exercise Class 11 Maths Question 20:
Solution:
Miscellaneous Exercise Class 11 Maths Question 21:
Solution:
Miscellaneous Exercise Class 11 Maths Question 22:
Solution:
Miscellaneous Exercise Class 11 Maths Question 23:
Solution:
Miscellaneous Exercise Class 11 Maths Question 24:
Solution:
Miscellaneous Exercise Class 11 Maths Question 25:
Solution:
Miscellaneous Exercise Class 11 Maths Question 26:
Solution:
Miscellaneous Exercise Class 11 Maths Question 27:
Solution:
Miscellaneous Exercise Class 11 Maths Question 28:
Solution:
Miscellaneous Exercise Class 11 Maths Question 29:
Solution:
Miscellaneous Exercise Class 11 Maths Question 30:
Miscellaneous Exercise Class 11 Maths Question 31:
Solution:
Miscellaneous Exercise Class 11 Maths Question 32:
Solution:
Miscellaneous Exercise Class 11 Maths Question 33:
Solution:
Miscellaneous Exercise Class 11 Maths Question 34:
Solution:
Solution:
Miscellaneous Exercise Class 11 Maths Question 36:
Solution:
Miscellaneous Exercise Class 11 Maths Question 37:
Solution:
Miscellaneous Exercise Class 11 Maths Question 38:
Solution:
Miscellaneous Exercise Class 11 Maths Question 39:
Solution:
Miscellaneous Exercise Class 11 Maths Question 40:
Solution:
Miscellaneous Exercise Class 11 Maths Question 41:
Solution:
Miscellaneous Exercise Class 11 Maths Question 42:
Solution:
Miscellaneous Exercise Class 11 Maths Question 43:
Solution:
Miscellaneous Exercise Class 11 Maths Question 44:
Solution:
Move to Top →Class 12 Integrals Chapter 7
Integration Formulas
Move to Top →Class 12 Integrals Chapter 7
गणित कक्षा 12 समाकलन प्रश्नावली 7.1
निम्नलिखित फलनों के प्रतिअवकलज ( समाकलन) निरीक्षण विधि द्वारा ज्ञात कीजिए।
Ex 7.1 Class 11 Maths प्रश्न 1.
sin 2x
हल-
∫sin 2x dx
हम जानते हैं कि, cos2x = -2 sin 2x
या sin 2x = cos2x
sin 2x = (cos2x)
अतः sin 2x का प्रति अवकलज cos 2x है।
Ex 7.1 Class 11 Maths प्रश्न 2.
cos 3x
हल-
∫cos 3x dx
हम जानते हैं कि, sin 3x = 3 cos 3x
अत: cos3x का प्रति अवकलज sin 3x हैं।
Ex 7.1 Class 11 Maths प्रश्न 3.
e2x
हल-
∫e2xdx
हम जानते हैं कि,
Ex 7.1 Class 11 Maths प्रश्न 4.
(ax + b)²
हल-
∫(ax + b)² dx
हम जानते हैं कि,
Ex 7.1 Class 11 Maths प्रश्न 5.
sin 2x – 4e3x
हल-
हम जानते हैं
निम्नलिखित समाकलनों को ज्ञात कीजिए।
Ex 7.1 Class 11 Maths प्रश्न 6.
∫(4e3x+ 1) dx
हल-
∫(4e3x+ 1) dx = 4∫e3xdx + ∫1 dx
Ex 7.1 Class 11 Maths प्रश्न 7.
हल-
Ex 7.1 Class 11 Maths प्रश्न 8.
∫(ax² + bx + c) dx
हल-
∫(ax² + bx + c) dx = a∫x²dx + b∫xdx + c∫1 dx
Ex 7.1 Class 11 Maths प्रश्न 9.
∫(2x² + ex) dx
हल-
∫(2x² + ex) dx = 2∫x² dx + ∫exdx
Ex 7.1 Class 11 Maths प्रश्न 10.
हल-
Ex 7.1 Class 11 Maths प्रश्न 11.
हल-
Ex 7.1 Class 11 Maths प्रश्न 12.
हल-
Ex 7.1 Class 11 Maths प्रश्न 13.
हल-
Ex 7.1 Class 11 Maths प्रश्न 14.
∫(1-x)√x dx
हल-
∫(1-x)√x dx
=∫(√x-x√x)dx
Ex 7.1 Class 11 Maths प्रश्न 15.
∫√x(3x² + 2x + 3)dx
हल-
∫√x(3x² + 2x + 3)dx
Ex 7.1 Class 11 Maths प्रश्न 16.
∫(2x – 3cosx + ex)dx
हल-
∫(2x – 3cosx + ex)dx
∫(2x² – 3sinx + 5√x)dx
हल-
∫(2x² – 3sinx + 5√x)dx
= 2∫x² dx – 3 ∫ sinx dx + 5∫√x dx
Ex 7.1 Class 11 Maths प्रश्न 18.
∫secx (sec x + tan x) dx
हल-
∫sec x (sec x + tan x) dx
= ∫(sec² x + sec x tan x) dx
= ∫(sec² x dx
= ∫sec x tan x dx
tan x + sec x + C
Ex 7.1 Class 11 Maths प्रश्न 19.
हल-
Ex 7.1 Class 11 Maths प्रश्न 20.
हल-
एवं 22 में सही उत्तर का चयन कीजिए
Ex 7.1 Class 11 Maths प्रश्न 21
हल-
Ex 7.1 Class 11 Maths प्रश्न 22
हल-
Move to Top →Class 12 Integrals Chapter 7
Updatedfor 2019 Exams.