List of top Mathematics Questions on Integral Calculus asked in AP ECET Metallurgical Eng

If $k \int_{0}^{1} x f(3x) dx = \int_{0}^{3} t f(t) dt$ then $k =$

$\int_{a}^{b} (|x-a| + |x-b|) dx = , (0 < a < b)$

$\int_{0}^{2} \frac{dx}{\sqrt{2+x} + \sqrt{2-x}} =$

If $\int \frac{1}{(x+100)\sqrt{x+99}} dx = f(x) + c$ then $f(x) =$

$\int \frac{1+\cos 4x}{\cot x - \tan x} dx =$

If $I_{n} = \int \frac{t^{n}}{1+t^{2}} dt$ then $I_{6} + I_{4} =$

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

If $\int \frac{2x^{2}+a^{2}}{x^{2}(x^{2}+a^{2})} dx = \frac{k}{x} + \frac{1}{a} \tan^{-1} \frac{x}{a} + c$ then $k =$

When $a=b$ then $\int_{a}^{b} f(x)dx =$

The area under the curve $f(x) = \sin x$ in $[0, 2\pi]$ is

If $f(x)$ is an even function, then $\int_{-a}^{a} f(x)dx=$

$\int_0^\pi dx =$

$\int \sin \frac{y}{2} \, dy =$

$\int \frac{dx}{\sqrt{x}} =$

$\int e^x \cos x \, dx =$

$\int \frac{1}{\sqrt{a^2 - x^2}} \, dx =$

$\int \cot^2 x \, dx =$