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evaluate ∫ cos^-1 ( sin x ) dx

evaluate
∫ cos^-1 ( sin x ) dx

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
10 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
askIITians Faculty 628 Points
4 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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