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

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

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

\[\int\limits_0^\pi \sin^3 x\left( 1 + 2 \cos x \right) \left( 1 + \cos x \right)^2 dx\]

\[\int\limits_0^\infty \frac{x}{\left( 1 + x \right)\left( 1 + x^2 \right)} dx\]

\[\int\limits_0^{\pi/4} \sin 2x \sin 3x dx\]

\[\int\limits_0^1 \sqrt{\frac{1 - x}{1 + x}} dx\]

\[\int\limits_1^2 \frac{1}{x^2} e^{- 1/x} dx\]

\[\int\limits_0^{\pi/4} \cos^4 x \sin^3 x dx\]

\[\int\limits_{\pi/3}^{\pi/2} \frac{\sqrt{1 + \cos x}}{\left( 1 - \cos x \right)^{5/2}} dx\]

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

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

Evaluate the following integrals :-

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

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

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

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

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

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

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

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

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