List of top Mathematics Questions on Definite Integral asked in AP EAPCET

Evaluate \[ \int_{1/e}^{e^2} \left| \frac{\log_e x}{x} \right| \,dx \]

Evaluate \[ I=\int_{-2}^{0} \Big(x^3+3x^2+3x+3+(x+1)\cos(x+1)\Big)\,dx \]

Evaluate $\int_0^{\pi/2} \sin^6 x \cos^4 x dx$

Evaluate $\lim_{n\to\infty} \frac{1}{n^2}\sum_{r=1}^n r e^{r/n}$

If \[ \int_0^1 (3x^2+2x+1)\,dx=k, \] then the value of \(k\) is

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

The value of the definite integral $\int_0^{\pi/2} \frac{\sin^{3/2} x}{\sin^{3/2} x + \cos^{3/2} x} \, dx$ is:

Assertion (A): \[ \int_{2}^{e}\left(\frac{1}{\log_e x}-\frac{1}{(\log_e x)^2}\right)\,dx = e-2\log_2 e \] Reason (R): \[ \int_{a}^{b} e^x\left(f(x)+f'(x)\right)\,dx = e^bf(b)-e^af(a) \]

If \[ \int_0^\pi \frac{dx}{1+2\sin^2x}=k, \] then greatest integer less than or equal to \(k\) is

Evaluate \[ \int_0^{\pi^2/4}\left(2\sin\sqrt{x}+\sqrt{x}\cos\sqrt{x}\right)\,dx \]

Evaluate \[ \int_{0}^{\pi}\frac{x}{\sin x}\left(3\cos^2x+2\sin x+\sin^3x-3\right)\,dx \] is equal to:

If \([\,\cdot\,]\) represents greatest integer function, then \[ \int_{\frac{3\pi}{4}}^{\pi} \left[\sin x+\left[\frac{4x}{\pi}\right]\right]\,dx = \] is equal to:

Evaluate \[ \int_{0}^{\pi} \left( \cos^2\left(\frac{3\pi}{8}-\frac{x}{4}\right) - \cos^2\left(\frac{11\pi}{8}+\frac{x}{4}\right) \right)\,dx \] is equal to:

\([\,.\,]\) represents a greatest integer function. If \[ \int_{\sqrt{3}}^{\sqrt{18}}[x]\,dx=a+b\sqrt{2}+c\sqrt{3}, \] then \[ a+b+c= \] is:

Evaluate \[ \int_{0}^{4}\frac{x+2}{\sqrt{4x-x^2}}\,dx \] is:

If \[ \int_1^3 x\sqrt[n]{x^2-1}\,dx=6, \] then \(n=\)

If \([\,\,]\) represents greatest integer function, then \[ \int_{-1}^{1}\left(x[1+\sin \pi x]+1\right)dx= \]

If \[ \lim_{n\to\infty} \left[ \frac{n}{(n+1)\sqrt{2n+1}} + \frac{n}{(n+2)\sqrt{2(2n+2)}} + \frac{n}{(n+3)\sqrt{3(2n+3)}} +\cdots+n\ \text{terms} \right] = \int_0^1 f(x)\,dx, \] then \(f(x)=\)

If \[ f(x)=\max\{\sin x,\cos x\} \] and \[ g(x)=\min\{\sin x,\cos x\}, \] then \[ \int_0^{\pi} f(x)\,dx+\int_0^{\pi} g(x)\,dx= \]

If \[ I_n=\int_{0}^{\pi/4}\tan^n x\,dx, \] then \[ \frac{1}{I_2+I_4}+\frac{1}{I_3+I_5}+\frac{1}{I_4+I_6} \] is equal to

Evaluate \[ \int_{0}^{\pi/4} e^{\tan^2\theta}\sin^2\theta\tan\theta\,d\theta \]

Evaluate \[ \int_{\pi/4}^{5\pi/4}\left(|\cos t|\sin t+|\sin t|\cos t\right)\,dt \]

\(\displaystyle \int_{-1}^{2}\left[\tan^{-1}\left(\frac{x}{x^2+1}\right)+\tan^{-1}\left(\frac{x^2+1}{x}\right)\right]dx=\)

\(\displaystyle \int_{-\pi/2}^{2\pi}\sin^{-1}(\sin x)\,dx=\)

If \(\displaystyle \int_{9}^{x}\frac{f(y)}{y^2}\,dy=2\sqrt{x}-6\), then \(f(x)=\)