List of top Mathematics Questions on integral asked in VITEEE

Evaluate the integral \( \displaystyle \int \frac{1}{x\log x}\,dx \).

Consider a curve \( y = y(x) \) in the first quadrant as shown in the figure. Let the area \( A_1 \) be twice the area \( A_2 \). The normal to the curve perpendicular to the line \[ 2x - 12y = 15 \] does NOT pass through which point? 
 

The value of the integral \[ \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \] is:

If sin y = x sin (a + y), then  dydxis
The solution of $\frac{dv}{dt} +\frac{k}{m}v = -g$ is
Value of $\int\limits_{0}^{\pi /2} \frac{\sqrt{sin x}}{\sqrt{sin x}\sqrt{cos x}} $ dx is
If $f(x) = x^2 , g(x) = 2x,0 \leq x \leq 2$ then the value of $I(x) = \int\limits_0^2 max (f(x), g(x))$ is
The solution of $\frac{dy}{dx} = \frac{x^{2} + y^{2} + 1}{2xy}$, satisfying $ y\left(1\right) = 0$ is given by

The solution of $(D^2 + 16)$ $y = cos4x$ is