List of top Mathematics Questions on Some Properties of Definite Integrals asked in JEE Advanced

The value of the definite integral \( \int_0^2 \frac{1}{3^x + 3} dx \) is
Evaluate the definite integral: \[ I = \int_{\frac{1}{2}}^{2} \frac{\tan^{-1} x \, dx}{2x^2 - 3x + 2} \]
The value(s ) of $ \int^1_0 \frac { x^4 ( 1 - x )^4 }{ ( 1 + x^2 ) } \, dx $ is are
The value of the integral $ \int^{ \pi / 2 }_ 0 \frac {\sqrt { \cot \, x }}{ \sqrt { \cot \, x } + \sqrt { \tan \, x }} \, dx \, is $