List of top Mathematics Questions on Definite and indefinite integrals asked in AP EAPCET

The value of the integral \( \int_{0}^{4} ||x - 2| - x| dx = \)
If \( [ ] \) denotes the greatest integer function, then \( \int_{1}^{2} [x^2] dx = \)
Let the function $ f(x) $ be defined as $ f(x) = \frac{x - |x|}{x} $, then:
Let \[ f(x)=\int \frac{\sqrt{x}}{(1+x)^2}\,dx \quad (x\geq 0) \] Then \[ f(3)-f(1) \] is equal to:
Evaluate the integral \[ I = \int_{-1}^{1} \left( \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right) \, dx \]
Evaluate the integral $$ \int_{0}^{\frac{\pi}{4}} \frac{x^2}{(x \sin x + \cos x)^2} dx. $$
Evaluate the integral \[ I = \int_1^5 \left( |x - 3| + |1 - x| \right) \, dx \]
\( \int_{-4\pi}^{4\pi} \tan^9 x \sin^6 x \cos^3 x \, dx = \)
Given that $\frac{d}{dx} \int_{0}^{\phi(x)} f(t) dt = f(\phi(x)) \phi'(x)$. For all $x \in (0, \frac{\pi}{2})$, if $\int_{1}^{\cos x} t^2 f(t) dt = \cos 2x$, then $f\left(\frac{1}{\sqrt{2}}\right) =$
The area bounded by \( y - 1 = -|x| \) and \( y + 1 = |x| \) is:
If $[\cdot]$ denotes the greatest integer function, then $\int_{0}^{1000} e^{x - \lfloor x \rfloor} dx =$
Evaluate \[ \int_{\frac{\pi}{11}}^{\frac{9\pi}{22}} \frac{dx}{1+\sqrt{\tan x}} \]
If \(m,n\in \mathbb{Z}\), then \[ \int_0^{2\pi}\cos mx\cos nx\,dx+\int_{-\pi}^{\pi}\sin mx\cos nx\,dx= \]
Evaluate \[ \int_2^5 \sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\,dx \]
Evaluate \(\lim_{n \to \infty} \frac{1}{\sqrt{n}} \left[ 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \cdots + \frac{1}{\sqrt{n}} \right]\)
Evaluate \[ \int_{-\pi/4}^{\pi/4}\cos^{-8}x\,dx \]
Evaluate \[ \int_{a-1}^{a}\frac{e^x(a-x)}{(x-a+1)^2}\,dx \]
For \(n\in N\), if \[ I_n=\int \frac{\sin nx}{\sin x}\,dx = \frac{2}{n-1}\sin(n-1)x+I_{n-2} \] and \[ \int_0^\pi \frac{\sin nx}{\sin x}\,dx=\frac{k\pi}{2}, \] then \(k=\)
If \[ f(x)=\sin(\tan^{-1}x), \] then \[ \int_0^1 xf''(x)\,dx= \]
Find the value of \[ \lim_{n\to\infty}\left(\frac{1^2}{n^3+1^3}+\frac{2^2}{n^3+2^3}+\cdots+\frac{1}{2n}\right) \] =
If \[ \int f(x)\,dx=F(x)+C, \] then \[ \frac{d}{dt}\int_{g(t)}^{h(t)}f(x)\,dx= \]
If \[ \int_{0}^{\pi/2}\sin^m x\cos^4 x\,dx=\frac{7\pi}{2048}, \] then \(m=\)
Evaluate \[ \int_{-\pi}^{\pi}\frac{\cos^{2022}x}{1+(2022)^x}\,dx \] =
If \[ \int \frac{\cosec^2x-2022}{\cos^{2022}x}\,dx=f(x)+C \Rightarrow f\left(\frac{\pi}{4}\right)= \]
If \[ \int \cos^{-1}\left(\sqrt{\frac{x}{a+x}}\right)\,dx=f(x)+C \Rightarrow f'(a)= \]