List of top Mathematics Questions on Integration asked in TS EAMCET

The area of the region bounded by $y=x^3$, x-axis, $x=-2$ and $x=4$ is

If $\int_0^{\pi/2}\tan^{14}(x/2)dx = 2\left[\sum_{n=1}^7 f(n) - \frac{\pi}{4}\right]$, then $f(n)=$

If $I_1 = \int \frac{e^x}{e^{4x}+e^{2x}+1}dx$, $I_2 = \int \frac{e^{-x}}{e^{-4x}+e^{-2x}+1}dx$, then $I_2-I_1=$

If $\int \frac{\sqrt{1-\sqrt{x}}}{\sqrt{x(1+\sqrt{x})}}dx = 2f(x)-2\sin^{-1}\sqrt{x}+c$, then $f(x)=$

If $\int \frac{3x+2}{4x^2+4x+5}dx = A\log(4x^2+4x+5)+B\tan^{-1}(\frac{2x+1}{2})+c$, then $A+B=$

Consider the following
Assertion (A): $\int \sqrt{x-3}(\sin^{-1}(\log x) + \cos^{-1}(\log x))dx = \frac{\pi}{3}(x-3)^{3/2}+c$
Reason (R): $\sin^{-1}(f(x))+\cos^{-1}(f(x))=\frac{\pi}{2}$, $|f(x)|\le 1$
The correct answer is

$\lim_{n \to \infty} \frac{(2n(2n-1)...(n+2)(n+1))^{1/n}}{n} =$

$\int_{-2}^{4} |2-x^2| dx =$

$\int \frac{3^x(x\log 3 - 1)}{x^2} dx =$

If $\frac{5\pi}{4}<x<\frac{7\pi}{4}$, then $\int \sqrt{\frac{1-\sin 2x}{1+\sin 2x}} dx =$

$\int x\text{Tan}^{-1}\sqrt{\frac{1+x^2}{1-x^2}}dx=$

$\int \frac{1}{(2\cos x + \sin x)^2} dx =$

$\int_{-1}^{1} \frac{\log 2 - \log(1+x)}{\sqrt{1-x^2}} dx =$

$\int_{0}^{\pi/4} \frac{\sec x}{3\cos x + 4\sin x} dx =$

If $[\cdot]$ denotes the greatest integer function, then $\int_1^2 [x^2] dx =$

$\int_4^{18} \frac{1}{(x+2)\sqrt{x-3}}dx = $

$\int_0^{\pi/2} \frac{1}{5\cos^2 x + 16\sin^2 x + 8\sin x \cos x} dx =$

$\int \frac{\log x}{(1+x)^2}dx = $

$\int \frac{x\text{Tan}^{-1}x}{(1+x^2)^2}dx =$

$\int(1+\tan^2 x)(1+2x\tan x)dx =$

$\int e^x(x^3-2x^2+3x-4)dx =$