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

\[\int\limits_0^1 \log\left( 1 + x \right) dx\]

Evaluate the following integrals :-

\[\int_2^4 \frac{x^2 + x}{\sqrt{2x + 1}}dx\]

\[\int\limits_0^1 x \left( \tan^{- 1} x \right)^2 dx\]

\[\int\limits_0^1 \left( \cos^{- 1} x \right)^2 dx\]

\[\int\limits_1^2 \frac{x + 3}{x\left( x + 2 \right)} dx\]

\[\int\limits_0^{\pi/4} e^x \sin x dx\]

\[\int\limits_0^{\pi/4} \tan^4 x dx\]

\[\int\limits_0^1 \left| 2x - 1 \right| dx\]

\[\int\limits_1^3 \left| x^2 - 2x \right| dx\]

\[\int\limits_0^{\pi/2} \left| \sin x - \cos x \right| dx\]

\[\int\limits_0^1 \left| \sin 2\pi x \right| dx\]

\[\int\limits_1^3 \left| x^2 - 4 \right| dx\]

\[\int\limits_{- \pi/2}^{\pi/2} \sin^9 x dx\]

\[\int\limits_{- 1/2}^{1/2} \cos x \log\left( \frac{1 + x}{1 - x} \right) dx\]

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

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

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

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

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

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