## 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) = x^{5} cos^{2} x

Now f (-x) = (- x)^{5} cos^{2} (- x)

= – x^{5} cos^{2} 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 = sec^{2} 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:

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