NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11.
- Integrals Class 12 Ex 7.1
- Integrals Class 12 Ex 7.2
- Integrals Class 12 Ex 7.3
- Integrals Class 12 Ex 7.4
- Integrals Class 12 Ex 7.5
- Integrals Class 12 Ex 7.6
- Integrals Class 12 Ex 7.7
- Integrals Class 12 Ex 7.8
- Integrals Class 12 Ex 7.9
- Integrals Class 12 Ex 7.10
Board | CBSE |
Textbook | NCERT |
Class | Class 12 |
Subject | Maths |
Chapter | Chapter 7 |
Chapter Name | Integrals |
Exercise | Ex 7.11 |
Number of Questions Solved | 21 |
Category | NCERT Solutions |
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11
By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19.
Ex 7.11 Class 12 Maths Question 1.
Solution:
Ex 7.11 Class 12 Maths Question 2.
Solution:
let I =
Ex 7.11 Class 12 Maths Question 3.
Solution:
let I =
Ex 7.11 Class 12 Maths Question 4.
Solution:
let I =
Ex 7.11 Class 12 Maths Question 5.
Solution:
at x = – 5, x + 2 < 0; at x = – 2, x + 2 = 0; at x = 5, x + 2>0;x + 2<0, x + 2 = 0, x + 2>0
Ex 7.11 Class 12 Maths Question 6.
Solution:
Ex 7.11 Class 12 Maths Question 7.
Solution:
Ex 7.11 Class 12 Maths Question 8.
Solution:
let I =
Ex 7.11 Class 12 Maths Question 9.
Solution:
let 2-x = t
⇒ – dx = dt
when x = 0, t = 2 and when x = 2,t = 0
Ex 7.11 Class 12 Maths Question 10.
Solution:
Ex 7.11 Class 12 Maths Question 11.
Solution:
Let f(x) = sin² x
f(-x) = sin² x = f(x)
∴ f(x) is an even function
Ex 7.11 Class 12 Maths Question 12.
Solution:
let I = …(i)
Ex 7.11 Class 12 Maths Question 13.
Solution:
Let f(x) = sin7 xdx
⇒ f(-x) = -sin7 x = -f(x)
⇒ f(x) is an odd function of x
⇒
Ex 7.11 Class 12 Maths Question 14.
Solution:
let f(x) = cos5 x
⇒ f(2π – x) = cos5 x
Ex 7.11 Class 12 Maths Question 15.
Solution:
let I = …(i)
Ex 7.11 Class 12 Maths Question 16.
Solution:
let I =
then I =
Ex 7.11 Class 12 Maths Question 17.
Solution:
let I = …(i)
Ex 7.11 Class 12 Maths Question 18.
Solution:
Ex 7.11 Class 12 Maths Question 19.
show that if f and g are defined as f(x)=f(a-x) and g(x)+g(a-x)=4
Solution:
let I =
Ex 7.11 Class 12 Maths Question 20.
The value of is
(a) 0
(b) 2
(c) π
(d) 1
Solution:
(c) let I = is
Ex 7.11 Class 12 Maths Question 21.
The value of is
(a) 2
(b)
(c) 0
(d) -2
Solution:
let I =
We hope the NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11 help you. If you have any query regarding NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11, drop a comment below and we will get back to you at the earliest.