Subject

Mathematics

Class

JEE Class 12

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JEE Mathematics Solved Question Paper 2015

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Multiple Choice Questions

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31.
$\int e^{x} (\frac{1 + \sin (x)}{1 + \cos (x)}) dx$ is equal to

e^x+ C

$e^{x} \tan (\frac{x}{2}) + C$

$e^{x} \sin (x) + C$

$\tan (\frac{x}{2}) + C$

B.

$e^{x} \tan (\frac{x}{2}) + C$

$Let I = \int e^{x} (\frac{1 + \sin (x)}{1 + \cos (x)}) dx = \int e^{x} (\frac{1 + 2 \sin (\frac{x}{2}) \cos (\frac{x}{2})}{2 \cos^{2} (\frac{x}{2})}) dx = \int e^{x} (\frac{1}{2} \sec^{2} (\frac{x}{2}) + \tan (\frac{x}{2})) dx = e^{x} \tan (\frac{x}{2}) + C [∵ e^{x} [f (x) + f' (x)] dx = e^{x} f (x) + C]$

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32.

$\int_{- \frac{π}{4}}^{\frac{π}{4}} \frac{dx}{1 + \cos (2 x)}$ is equal to

4
2
0
1

3
4

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