RBSE Solutions for Class 12 Maths Chapter 10 Definite Integral Ex 10.3

Rajasthan Board RBSE Class 12 Maths Chapter 10 Definite Integral Ex 10.3

Find the value of the following integrals :

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.
\(\int_{0}^{3}\) [x] dx, where [.] is greatest integer function.
Solution:

Question 5.

Solution:

Here f (x) = x⁵ cos² x
Now f (-x) = (- x)⁵ cos² (- x)
= – x⁵ cos² x
= -f(x)
Thus, this is an odd function.

Question 6.

Solution:

[∵ sin x is odd function and cos x is even function
∴ sin (- x) = – sin x
cos (- x) = cos x]
= -f (x)
Thus this is a odd function

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:


Where t = tan x and dt = sec² x dx
When x = 0, then
t = tan 0 = 0
When x = \(\frac { \pi }{ 4 } \),then t = tan \(\frac { \pi }{ 4 } \) = 1

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.

Solution:

RBSE Solutions for Class 12 Maths