List of top Mathematics Questions on Definite Integral asked in KCET

$$ \int_{0}^{\pi/4} (\tan^8 x + \tan^6 x) \, dx = ? $$
$$ \int_{-\pi/4}^{\pi/4} \sin^{103} x \cos^{101} x \, dx = ? $$
One of the possible functions $f(x)$ which satisfies $\int_{-2}^{2} f(x) dx = 0$ is
$\int_{a-6}^{b-6} f(x + 6) dx$ is equal to
\(\int\sqrt{\cosec x-\sin x}\ dx=\)
\(\int\sqrt{5-2x+x^2}\ dx=\)
\(\int\limits_{-2}^{0}(x^3+3x^2+3x+3+(x+1)\cos(x+1))\ dx=\)
\(\int\limits_{2}^{8}\frac{5^{\sqrt{10-x}}}{5^{\sqrt{x}}+5^{\sqrt{10-x}}}\ dx=\)
\(\int\limits_{0}^1\frac{xe^x}{(2+x)^3}\ dx\) is equal to
If \([x]\) is the greatest integer function not greater than x, then \(\int [x]\)\(dx\) is equal to
\(\int\limits_{0}^{\frac{\pi}{2}}\frac{\cos x\sin x}{1+\sin x}\ dx\) is equal to
Evaluate \(\int\limits_{2}^3x^2\ dx\) as the limit of a sum
\(\int \frac{\cos(2x) - \cos(2\alpha)}{\cos(x) - \cos(\alpha)} \, dx\) is equal to
\(\int\limits_{0}^{\frac{\pi}{2}}\sqrt{\sin \theta}\cos^3\theta\ d\theta\) is equal to
The value of \(\int\limits_0^{4042}\frac{\sqrt{x}\ dx}{\sqrt{x}+\sqrt{4042-x}}\) is equal to
If \(I_n=^{\frac{\pi}{4}}_0\int\tan^n x\ dx\) where n is positive integer then I10 + I8 is equal to
The value of \(\int e^x[\frac{1+\sin x}{1+\cos x}]dx\) is equal to
The value of \(\int\frac{xe^x dx}{(1+x)^2}\) is equal to
The value of \(\int\frac{x^2dx}{\sqrt{x^6+a^6}}\) is equal to
\(\int\frac{x^3\sin(\tan^{-1}(x^4))}{1+x^8}dx\) is equal to

The value of 

\[\int e^{\sin x}\sin 2x\ dx\]

 is

The value of \(\int\limits_0^1\frac{\log(1+x)}{1+x^2}\ dx\) is
The value of \(\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{\cos x}{1+e^x}\ dx\) is
The value of \(\int\limits^{\frac{1}{2}}_{-\frac{1}{2}}\cos^{-1}x\ dx\) is
The value of \(\int\frac{1+x^4}{1+x^6}dx\) is