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1
BITSAT 2025
MCQ (Single Correct Answer)
+3
-1

What is the value of the definite integral $\int_0^\pi \log (\sin x) d x$ ?

A

$-\frac{\pi}{4} \log 2$

B

$-\frac{\pi}{2} \log 2$

C

$-\pi \log 2$

D

$-\frac{\pi}{4} \log \left(\frac{1}{2}\right)$

2
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
$ \int_{0}^{\infty} \frac{d x}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)} $ is
A
$ \frac{\pi a b}{a+b} $
B
$ \frac{a b}{2(a+b)} $
C
$ \frac{\pi}{2 a b(a+b)} $
D
$ \frac{\pi(a+b)}{2 a b} $
3
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
The value of definite integral $ \int_{0}^{\pi / 2} \log (\tan x) d x $ is .
A
0
B
$ \frac{\pi}{4} $
C
$ \frac{\pi}{2} $
D
$ \pi $
4
BITSAT 2021
MCQ (Single Correct Answer)
+3
-1

$$\int\limits_0^1 {{{\log (1 + x)} \over {1 + {x^2}}}dx} $$ is equal to :

A
$${\pi \over 8}\log 2$$
B
$${\pi \over 8}\log {1 \over 2}$$
C
$${\pi \over 4}\log 2$$
D
None of these
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