Find the integration of -e-sin-1x-1-x-2-dxe-sin-1x-Ce-sin-1x-Ce-sin-1x-2-Ce-sin x-C

The correct option is A e^sin^ 1x+CGiven, nbsp;∫e^sin^ 1x√(1 x^2).dx Let t= sin^ 1x dt = 1√(1 x^2).dx ⇒ dx=(√(1 x^2)).dt Putting these value in above integr ...

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Standard XII

Physics

Examples

Find the inte...

Question

Find the integration of $\int \frac{e^{{sin}^{- 1} x}}{\sqrt{1 - x^{2}}} . d x$

e^{{sin}^{- 1} x} + C

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e^{- {sin}^{- 1} x} + C

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\frac{e^{{sin}^{- 1} x}}{2} + C

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e^{sin x} + C

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Solution

The correct option is A $e^{{sin}^{- 1} x} + C$
Given, $\int \frac{e^{{sin}^{- 1} x}}{\sqrt{1 - x^{2}}} . d x$

Let $t = {sin}^{- 1} x$
$⟹ d t = \frac{1}{\sqrt{1 - x^{2}}} . d x$
$\Rightarrow d x = (\sqrt{1 - x^{2}}) . d t$
Putting these value in above integration
$∴$ we have $I = \int e^{t} . d t = e^{t} + C$
$∴$ $I = e^{{sin}^{- 1} x} + C$

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Find the integration of ∫esin−1x√1−x2.dx

The correct option is A esin−1x+CGiven, ∫esin−1x√1−x2.dx Let t=sin−1x ⟹dt=1√1−x2.dx ⇒dx=(√1−x2).dt Putting these value in above integration ∴ we have I=∫et.dt=et+C ∴ I=esin−1x+C

Find the integration of $\int \frac{e^{{sin}^{- 1} x}}{\sqrt{1 - x^{2}}} . d x$