List of top Mathematics Questions on Integration asked in AP EAPCET

The area of the region (in sq.units) bounded by the curves \(x^2 + y^2 = 16\) and \(x^2 + y^2 = 6x\) is?
\( \int_{5\pi}^{25\pi} |\sin 2x + \cos 2x| \ dx = \)
If $$ \int \frac{dx}{1 - \sin^4 x} = A \tan x + B \tan^{-1}(\sqrt{2} \tan x) + C, $$ then find $ A^2 - B^2 $.
Evaluate the limit: \[ \lim_{n \to \infty} \left[ \frac{1}{n^2} \sec^2 \frac{1}{n^2} + \frac{2}{n^2} \sec^2 \frac{4}{n^2} + \frac{3}{n^2} \sec^2 \frac{9}{n^2} + .s + \frac{1}{n^2} \sec^2 1 \right] = \]
The general solution of the differential equation \( \left(x \sin \frac{y}{x} \right) dy = \left( y \sin \frac{y}{x} - x \right) dx \) is
\( \int \frac{dx}{(1+\sqrt{x}) \sqrt{x-x^2}} = \)
Evaluate the definite integral: \[ \int_0^1 \frac{2x + 5}{x^2 + 3x + 2} \, dx = \]
Evaluate \[ \int \sin^3 x \cos^2 x \, dx = ? \]
Evaluate \[ \int \frac{1}{x^4 + 1} \, dx = ? \]
Evaluate \[ \int (\log 2x)^3 \, dx = ? \]
Evaluate the integral: \[ \int \left[\frac{1}{\cos x} - \frac{1}{\sin x} - \frac{1}{\sin x + 3\cos x}\right] dx \]
Evaluate the integral: \[ \int \frac{x+1}{x^3 - 1}dx \]
Evaluate the integral: \[ \int \frac{x^4-16x^2+2x+8}{x^3-4x^2+2}dx \]
\( \int \sqrt{x^2+x+1} \ dx \)
\( \int_{0}^{\pi/4} \frac{\cos^2 x}{\cos^2 x + 4\sin^2 x} dx = \)
\( \int_{5\pi}^{25\pi} |\sin 2x + \cos 2x| \ dx = \)
\( \int \left( \sum_{r=0}^{\infty} \frac{x^r 2^r}{r!} \right) dx = \)
Evaluate the integral: \[ I = \int_{\pi/6}^{\pi/3} \cos^{-4} x \, dx \]
Evaluate the integral: \[ I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx \]
Evaluate the integral: \[ \int \frac{x+1}{x^3 - 1}dx \]
Evaluate the integral: \[ \int \frac{x^4-16x^2+2x+8}{x^3-4x^2+2}dx \]
Evaluate the integral: \[ \int \operatorname{Cos}^{-1} \left( \frac{1-x^2}{1+x^2} \right) dx \]
\( \int_{0}^{\pi/4} \frac{\cos^2 x}{\cos^2 x + 4\sin^2 x} dx = \)
\( \int \frac{13\cos 2x - 9\sin 2x}{3\cos 2x - 4\sin 2x} dx = \)
\( \int \sqrt{x^2+x+1} \ dx \)