List of top Mathematics Questions on integral asked in BITSAT

Evaluate the integral: $$ \int_0^{\pi/4} \frac{\ln(1 + \tan x)}{\cos x \sin x} \, dx $$

Evaluate the integral \( \int_0^1 \frac{\ln(1 + x)}{1 + x^2} \, dx \)

The area enclosed by the curves \( y = x^3 \) and \( y = \sqrt{x} \) is:

The value of \( \int_0^{\frac{\pi}{2}} \frac{\sin\left( \frac{\pi}{4} + x \right) + \sin\left( \frac{3\pi}{4} + x \right)}{\cos x + \sin x} \, dx \) is:

Evaluate the integral: \[ \int \frac{x^2 (x \sec^2 x + \tan x)}{(x \tan x + 1)^2} dx \]

Evaluate the integral: \[ \int_{5}^{9} \frac{\log 3x^2}{\log 3x^2 + \log (588 - 84x + 3x^2)} dx \]

The value of definite integral \( \int_0^{\pi/2} \log(\tan x) dx \) is:

The value of \( \int_0^\infty \frac{dx}{(x^2 + a^2)(x^2 + b^2)} \) is:

The value of \( \int e^{\tan \theta} (\sec \theta - \sin \theta) \, d\theta \) is:

Evaluate the integral: \[ \int \sqrt{x + \sqrt{x^2 + 2}} \, dx. \]

Evaluate the integral: \[ \int \frac{x^3 - 1}{x^3 + x} dx \]

Consider the function \( f(x) = \frac{|x - 1|}{x^2} \). Then \( f(x) \) is:

The function \[ f(x) = \frac{\cos x}{\left\lfloor \frac{2x}{\pi} \right\rfloor + \frac{1}{2}}, \] where \( x \) is not an integral multiple of \( \pi \) and \( \lfloor \cdot \rfloor \) denotes the greatest integer function, is: