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Grade 12Integral Calculus

evaluate
∫ cos^-1 ( sin x ) dx

taniska

11 Years agoGrade 12

2 Answers

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int cos^{-1}(sinx)dx$
$sin^{-1}x+cos^{-1}x = \frac{\pi }{2}$
$I = \int (\frac{\pi }{2} - sin^{-1}(sinx))dx$
$I = \int (\frac{\pi }{2} - x)dx$
$I = \int \frac{\pi }{2}dx - \int xdx$
$I = \frac{\pi }{2}x - \int xdx$
$I = \frac{\pi }{2}x - \frac{x^2}{2}+c$

Kushagra Madhukar

5 Years ago

Dear student,

Please find the solution to your problem.

In the given integral-

cos^-1(sinx) = π/2 – sin^-1(sinx) = π/2 – x

Hence, I = ∫(π/2 – x)dx

= π/2 x – x²/2 + c

Thanks and regards,

Kushagra

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