# RBSE Solutions for Class 12 Maths Chapter 10 Definite Integral Miscellaneous Exercise

## Rajasthan Board RBSE Class 12 Maths Chapter 10 Definite Integral Miscellaneous Exercise

Question 1.
The value

(a) 2 $$\int_{0}^{a}$$ sin 3x.x dx
(b) 0
(c) a2
(d) 1
Solution:

Question 2.

(a) 3
(b) 2
(c) $$\frac { 3 }{ 2 }$$
(d) $$\frac { 1 }{ 2 }$$
Solution:

Question 3.

Solution:
Option (b) is correct

Question 4.
If A(x) = $$\int_{x}^{0}$$ θ2 dθ, then value of A(3) will be :
(a) 9
(b) 27
(c) 3
(d) 81
Solution:

Thus Option (a) is correct

Question 5.

Solution:

Question 6.

Solution:

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:

and x = cot θ ∴ dx = – cosec2 θ dθ
when x = 0, then θ = $$\frac { \pi }{ 2 }$$
when x = ∞, then θ = 0

Question 16.

Solution:

Question 17.
Prove that

Solution:
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