Explanation for the correct optionEvaluate :∫sin^ 1(cos 3x)dxconsider the given Equation asI=∫sin^ 1(cos 3x)dxWe know that,sinθ =cos(π/2 θ)0ex0excosθ =sin(π/2 θ ...

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Standard XII

Mathematics

Chain Rule of Differentiation

∫sin-1cos 3xd...

Question

$\int \sin^{- 1} (\cos 3 x) d x =$

$(\frac{3 π}{2}) x - (\frac{x^{2}}{2}) + c$

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$(\frac{π}{2}) x - (\frac{3 x^{2}}{2}) + c$

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$(\frac{3 π}{2}) x + (\frac{x^{2}}{2}) + c$

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$(\frac{π}{2}) x - (\frac{x^{3}}{2}) + c$

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Solution

The correct option is B
$(\frac{π}{2}) x - (\frac{3 x^{2}}{2}) + c$

Explanation for the correct option
Evaluate : $\int \sin^{- 1} (\cos 3 x) d x$
consider the given Equation as
$I = \int \sin^{- 1} (\cos 3 x) d x$
We know that,
$\sin θ = \cos (\frac{π}{2} - θ) \cos θ = \sin (\frac{π}{2} - θ)$
Then the integral becomes,
$I = \int \sin^{- 1} (\sin (\frac{π}{2} - 3 x)) d x I = \int (\frac{π}{2} - 3 x) d x I = (\frac{π}{2}) x - (\frac{3 x^{2}}{2}) + c$
Hence, the correct answer is Option B.

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∫sin-1cos3xdx=

The correct option is B π2x-3x22+cExplanation for the correct optionEvaluate :∫sin-1cos3xdxconsider the given Equation asI=∫sin-1cos3xdxWe know that,sinθ=cosπ2-θcosθ=sinπ2-θThen the integral becomes,I=∫sin-1sinπ2-3xdxI=∫π2-3xdxI=π2x-3x22+cHence, the correct answer is Option B.

$\int \sin^{- 1} (\cos 3 x) d x =$