List of top Mathematics Questions on Integral Calculus asked in KEAM

Evaluate the integral: \[ \int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{\sqrt{\tan x}}{1 + \sqrt{\tan x}} \, dx \]

Evaluate the integral: \[ \int \frac{x^2 - 1}{x^4 + 3x^2 + 1} \, dx \]

Evaluate the integral:

\[ \int \frac{4x \cos \left( \sqrt{4x^2 + 7} \right)}{\sqrt{4x^2 + 7}} \, dx \]

The integral

\[ \int \frac{\sec x}{(\sec x + \tan x)^2} \, dx \] is:

Evaluate the integral \[ \int_{-500}^{500} \ln \left( \frac{1000 + x}{1000 - x} \right) dx \]

The integral

\[ \int \frac{dx}{x^8 \left( 1 + x^7 \right)^{2/3}} \] is equal to:

The value of \(\displaystyle\int_{0}^{2}\frac{x^2}{(x^3+1)^2}dx\) is equal to

The area of the region bounded by the curves y = x² and y = √x is (in square units)