PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

\[\int\limits_{- a}^a \frac{x e^{x^2}}{1 + x^2} dx\]

\[\int\limits_0^{\pi/2} \frac{1}{1 + \cot^7 x} dx\]

\[\int\limits_0^{2\pi} \cos^7 x dx\]

\[\int\limits_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}} dx\]

\[\int\limits_0^{\pi/2} \frac{1}{1 + \tan^3 x} dx\]

\[\int\limits_0^\pi \frac{x \sin x}{1 + \cos^2 x} dx\]

\[\int\limits_0^\pi x \sin x \cos^4 x dx\]

\[\int\limits_0^\pi \frac{x}{a^2 \cos^2 x + b^2 \sin^2 x} dx\]

\[\int\limits_{- \pi/4}^{\pi/4} \left| \tan x \right| dx\]

\[\int\limits_0^{15} \left[ x^2 \right] dx\]

\[\int\limits_0^\pi \frac{x}{1 + \cos \alpha \sin x} dx\]

\[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x} dx\]

\[\int\limits_0^{\pi/2} \frac{\cos^2 x}{\sin x + \cos x} dx\]

\[\int\limits_0^\pi \cos 2x \log \sin x dx\]

\[\int\limits_0^\pi \frac{x}{a^2 - \cos^2 x} dx, a > 1\]

\[\int\limits_0^\pi \frac{x \tan x}{\sec x + \tan x} dx\]

\[\int\limits_2^3 \frac{\sqrt{x}}{\sqrt{5 - x} + \sqrt{x}} dx\]

\[\int\limits_0^{\pi/2} \frac{\sin^2 x}{\sin x + \cos x} dx\]

\[\int\limits_0^{\pi/2} \frac{x}{\sin^2 x + \cos^2 x} dx\]

\[\int\limits_{- \pi}^\pi x^{10} \sin^7 x dx\]