cos⁻¹x x ∈[-1,1] ,Find the integrals of the given function with respect to x.
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HELLO DEAR,
put cos-¹x = t so that x = cost and dx = -sint dt.
therefore, ∫cos-¹x dx = -∫t sint dt
= -[t .(-cost) - ∫1.(-cost) dt]
[integrating by parts]
= t cost - ∫cost dt
= tcost - sint + C
= xcos-¹x - √(1 - x²) + C.
[therefore, cost = x => sint = √(1 - x²)].
I HOPE ITS HELP YOU DEAR,
THANKS
put cos-¹x = t so that x = cost and dx = -sint dt.
therefore, ∫cos-¹x dx = -∫t sint dt
= -[t .(-cost) - ∫1.(-cost) dt]
[integrating by parts]
= t cost - ∫cost dt
= tcost - sint + C
= xcos-¹x - √(1 - x²) + C.
[therefore, cost = x => sint = √(1 - x²)].
I HOPE ITS HELP YOU DEAR,
THANKS
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