Mathematics

# Evaluate the following integral:$\int { \cfrac { { \left( { e }^{ \sin ^{ -1 }{ x } } \right) }^{ 2 } }{ \sqrt { 1-{ x }^{ 2 } } } } dx$

##### SOLUTION
Let

$t={\sin}^{-1}{x}\Rightarrow\,dt=\dfrac{dx}{\sqrt{1-{x}^{2}}}$

$\displaystyle\int{\dfrac{{\left({e}^{{\sin}^{-1}{x}}\right)}^{2}}{\sqrt{1-{x}^{2}}}dx}$

$=\displaystyle\int{{e}^{2t}dt}$

$=\dfrac{{e}^{2t}}{2}+c$

$=\dfrac{1}{2}{\left({e}^{{\sin}^{-1}{x}}\right)}^{2}+c$ where $t={\sin}^{-1}{x}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

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$\displaystyle \int_{0}^{\pi /2}x^{2}.\sin x dx=$
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• B. $\pi/2$
• C. $\pi+1$
• D. $\pi-2$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral as the limit of sum:
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Q3 Single Correct Medium
$\int \dfrac {\sin^{-1}x-\cos^{-1}x}{\sin^{-1}x+\cos^{-1}x}dx=$
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Q4 Subjective Medium
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