How to solve <msubsup> &#x222B;<!-- ∫ --> 0 1 </msubsup> <msubsup> &#x222B;<!

Isaiah Owens

Isaiah Owens

Answered question

2022-05-19

How to solve 0 1 0 1 1 x 1 y d x d y

Answer & Explanation

stormsteghj

stormsteghj

Beginner2022-05-20Added 11 answers

Since 1 x = ( 1 x ) 1 / 2 , an antiderivative of which is 2 3 ( 1 x ) 3 / 2 , you have
0 1 1 x d x = [ 2 3 ( 1 x ) 3 / 2 ] x = 0 x = 1 = 2 3
and therefore
0 1 1 x d x 0 1 1 y d y = ( 2 3 ) 2 = 4 9 .

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