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

Evaluate the integral \[ \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x}\,dx. \]

Evaluate \( \displaystyle \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x}\,dx \).

If the solution of \[ \left( 1 + 2e^\frac{x}{y} \right) dx + 2e^\frac{x}{y} \left( 1 - \frac{x}{y} \right) dy = 0 \] is \[ x + \lambda y e^\frac{x}{y} = c \quad \text{(where \(c\) is an arbitrary constant), then \( \lambda \) is:} \]

The area bounded by \( f(x) = x^2, 0 \leq x \leq 1 \), and \( g(x) = x + 2, 1 \leq x \leq 2 \) and x-axis is

If \( f(a + b - x) = f(x), \) then \( \int_a^b f(x) \, dx \) is

What is the area of a loop of the curve \( y = \sin 30^\circ \)?

If \( (m,n) \) is an integer solution of \( \int_1^\infty \left( 1 + y^2 \right) dy \), then the expression for \( (m, n) \) in terms of \( (m+1, n+1) \) is?

\( \int_0^\infty \left( \sin x + \left| \sin x \right| \right) dx \) is equal to?

The value of \( \int_0^\infty \left[ \sqrt{x} \right] dx \), where \( \left[ . \right] \) is the greatest integer function, is?

The value of the integral $\int\limits ^{1/2}_{-1/2}\left[\left(\frac{x+1}{x-1}\right)^{^2}+\left(\frac{x+1}{x-1}\right)^{^2}-2\right]^{^{1/2}}\:\:dx$ is

The area lying in the first quadrant and bounded by the circle \( x^2 + y^2 = 4 \), the line \( x = \sqrt{3}y \), and the \( x \)-axis is:

The value of the integral $\int\limits_{0}^{\frac{\pi}{2}} log \left(tan\,x\right)dx=$