Integrals class 12 important questions

Here are some good Integrals class 12 important questions for Mathematics.

1.   $\int  {e^x sin x} \; dx$
2.   $\int_{2}^{8} |x-5|dx$
3.  $\int_{0}^{\pi/4} \frac { sinx + cosx}{9 +16sin2x}dx$
4.  $\int { \frac {1}{sinx + sec x}} dx$
5. $ \int { \frac {1}{2+ cosx} } dx$
6.  $ \int { \sqrt {\frac {b-x}{b+x}} }  \; dx$
7. $\int_{0}^{1} tan^{-1}x \; dx$
8.  $ \int {x sinx} \; dx$

Solutions

1. $ \frac {2}{5} e^x \left ( \frac {sin2x}{2} – cos 2x \right ) + C$
2. 9
3. $ \frac {1}{40} log 9$
4.  $\frac {1}{2\sqrt {3}} log \left ( \frac {\sqrt {3} + sinx-cos x}{\sqrt {3} -sinx + cos x} \right ) + tan^{-1} \left (sinx + cosx \right) + C$
5. $\frac {2}{\sqrt {3}} tan^{-1} \left (\frac {tan \left (x/2 \right )}{\sqrt {3}} \right ) +C$
6. $b sin^ {-1} \frac{x}{b} + \sqrt {b^2 -x^2} +C$
7. $ \frac {\pi}{4} – \frac {1}{2} log 2 $
8. $ -x cos x + sin x + C$

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