## 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) a^{2}

(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) = \(\int_{x}^{0}\) θ^{2} 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 = – cosec^{2} θ dθ

when x = 0, then θ = \(\frac { \pi }{ 2 } \)

when x = ∞, then θ = 0

Question 16.

Solution:

Question 17.

Prove that

Solution: