Definite Integral of cos(x)/sqrt(sin(x)) from pi/6 to pi/2

Milton Anderson

Milton Anderson

Answered question

2022-09-04

Definite Integral of cos ( x ) / sin ( x ) from π / 6 to π / 2

Answer & Explanation

Gerardo Kent

Gerardo Kent

Beginner2022-09-05Added 12 answers

Use regular u-substitution:
u = sin x d u = cos x d x
π / 6 π / 2 1 u d u = π / 6 π / 2 ( u ) 1 / 2 d u = [ u 1 / 2 1 / 2 ] π / 6 π / 2 = [ 2 sin x ] π / 6 π / 2
= 2 sin ( π / 2 ) 2 sin ( π / 6 )
= 2 1 2 1 / 2 = 2 2 1 2 = 2 2 2 ( 2 2 ) = 2 2 2 2 = 2 2
So, π / 6 π / 2 cos x sin x d x = 2 2

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