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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.3
Find the integrals of the functions in Exercises 62 to 83.
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Question : 82 of 271
Marks: +1, -0
sin⁡−1(cos⁡x)\sin^{-1} (\cos x)
Solution:  
Let I=∫sin⁡−1(cos⁡x)dxI=\int \sin^{-1} (\cos x)dx =∫sin⁡−1[sin⁡(π2−x)]dx=\int \sin^{-1} \left[ \sin \left( \frac{\pi}{2} - x \right) \right] dx
=∫(π2−x)dx=\int \left( \frac{\pi}{2} - x \right) dx =π2∫dx−∫xdx=\frac{\pi}{2} \int dx - \int x dx
=πx2−x22+C=\frac{\pi x}{2} - \frac{x^2}{2} + C
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