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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $\int \frac{y}{9}$$t \tan (t^2)dt$

$(a)\;\log | \cos t^2 |+c \\(b)\;\frac{2}{9} \log | \sec t^2|+c \\(c)\;\frac{-2}{9} \sec t^2 +c \\ (d)\;None$

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A)
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$t^2=a$
differentiate with respect to
$2tdt=da$
$\large\frac{2}{9}$$ \int \tan a. d a $
=> $\large\frac{2}{9}$$ \log | \sec a |+c$
=> $ \large\frac{2}{9}$$ \log | \sec t^2|+c$
Hence b is the correct answer.

 

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