Question 1: Palette 1/6

BITSAT 2025 MCQ

The value of integral $\int_a^b e^x d x$ as limit of sums is

A

$e^a-e^b$

B

$e^b-e^a$

C

$e^b+e^a$

D

$-e^a-e^b$

Question 2: Palette 2/6

BITSAT 2025 MCQ

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

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

Question 3: Palette 3/6

BITSAT 2024 MCQ

$ \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} $

Question 4: Palette 4/6

BITSAT 2024 MCQ

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 $

Question 5: Palette 5/6

BITSAT 2021 MCQ

$\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

Question 6: Palette 6/6

BITSAT 2020 MCQ

The value of the definite integral $\int\limits_0^{\pi /2} {{{dx} \over {\tan x + \cot x + \cos ec\,x + \sec x}}} $

A

$1 - {\pi \over 4}$

B

$1 + {\pi \over 4}$

C

$\pi + {1 \over 4}$

D

None of these