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Integral Calculus> Please solve the attached problem in inte...

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Please solve the attached problem in integral calculus.

P S Hamshika , 6 Years ago

Grade 12

1 Answers

Sami Ullah

Last Activity: 6 Years ago

Its very easy just a few manipulations you’ll have to do.First I will just solve the integral and later apply the upper and lower limits.

$I=\int\frac{\sqrt{x}}{\sqrt{1-x^3}}.dx$

$Let$ $u=x^\frac{3}{2}$ $\Rightarrow$ $u^2=x^3$

$Then$ $du=\frac{3}{2}x^\frac{1}{2}.dx$

$\Rightarrow$ $\frac{2}{3}du=\sqrt{x}.dx$

$Now$ $substituting$ $values$ ,

$I=\int \frac{2}{3}\times \frac{1}{\sqrt{1-u^2}}.du$

$I= \frac{2}{3}\sin^{-1}(u)$

$I= \frac{2}{3}\sin^{-1}(x^\frac{3}{2})$

$Putting$ $values$ ,

$I= \frac{2}{3}[\sin^{-1}(1^\frac{3}{2})-\sin^{-1}(0)]$

$I= \frac{2}{3}[\frac{\pi }{2}-0]$

$I= \frac{\pi }{3}$

So the awnser is option (2).

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