Evaluate the iterated integral. int_0^(pi/2)int_0^(cos x)(1+sin x)dydx

psetancabyc

psetancabyc

Answered question

2022-12-17

Evaluate the iterated integral. 0 π / 2 0 cos x ( 1 + sin x ) d y d x

Answer & Explanation

Deacon Coffey

Deacon Coffey

Beginner2022-12-18Added 8 answers

Given integral 0 π / 2 0 cos x ( 1 + sin x ) d y d x = 0 π / 2 ( 1 + sin x ) [ y ] 0 cos x d x = 0 π / 2 ( 1 + sin x ) ( cos x 0 ) d x = [ 1 2 ( 1 + sin x ) 2 ] 0 π / 2 = 1 2 ( ( 1 + sin ( π / 2 ) ) 2 ( 1 + sin 0 ) ) 2 = 1 2 ( 4 1 ) = 3 2
1. Let u = 1 + sin x then d u = cos x d x. This substitution gives 1 2 u 2
Result
0 π / 2 0 cos x ( 1 + sin x ) d y d x = 3 2

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