Arts (English Medium) Class 12 - CBSE Question Bank Solutions

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

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

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

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

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

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

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

Evaluate the following integrals :-

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

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

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

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

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

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

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

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

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

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

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

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

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