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:
