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

May 22, 2019 by Fazal Leave a Comment

   

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

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