more integration of inverse trig

differentiate (xcos-1x)-sqrt(1-x^2) and use the result to evaluate the integration of cos-1dx between x=1 and x=0

similarily, prove that d/dx (xsin-1x)=sin-1x+x/(sqrt(1-x^2)). Hence find primitive of sin-1x and show that integration of sin-1x between x=1/2 and x=0 is pi/12+sqrt3/2-1

THankyou !

Quote:

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Originally Posted by christina

differentiate (xcos-1x)-sqrt(1-x^2) and use the result to evaluate the integration of cos-1dx between x=1 and x=0

similarily, prove that d/dx (xsin-1x)=sin-1x+x/(sqrt(1-x^2)). Hence find primitive of sin-1x and show that integration of sin-1x between x=1/2 and x=0 is pi/12+sqrt3/2-1

THankyou !

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Have you done either of those derivatives? Once you have, the integrals should be obvious.