How do I find the following integral: int_0^1 x sqrt(1-x^2)dx

Alfredo Cooley

Alfredo Cooley

Answered question

2022-11-05

How do I find the following integral:
0 1 x   1 x 2 d x

Answer & Explanation

Waldruhylm

Waldruhylm

Beginner2022-11-06Added 14 answers

0 1 x   1 x 2 = 0 1   x ( 1 x 2 ) 1 / 2 d x
Let u = 1 x 2 . Then d u = 2 x d x x d x = 1 2 d u
Bounds of integration: At x=0, u=1, and x=1, u=0
Substituting gives us:
0 1   x   ( 1 x 2 ) 1 / 2 d x = 1 0   u 1 / 2 ( 1 2 d u ) = 1 2 1 0   u 1 / 2 d u = 1 2 u 3 / 2 | 1 0 = 1 2 u 3 / 2 | 0 1 = 1 2 ( 1 0 ) = 1 2

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