Simplify. int_0^2 2pi y((y^2)/2)) -((y^4)/4- (y^2)/2)dy

vangstosiis 2022-07-27 Answered
Simplify.
0 2  2 π y ( ( y 2 2 ) ( y 4 4 y 2 2 ) ) d y
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Answers (2)

abortargy
Answered 2022-07-28 Author has 19 answers
0 2 2 π y ( ( y 2 2 ) ( y 4 4 y 2 2 ) ) d y
= 0 2 2 π y ( y 2 2 y 4 4 + y 2 2 ) d y = 2 π 0 2 y ( 2 y 2 2 y 4 4 ) d y
= 2 π 0 2 y ( y 2 1 4 y 4 ) d y = 2 π 0 2 ( y 3 1 4 y 5 ) d y = 2 π [ y 4 4 1 4 y 6 6 ] 0 2
= 2 π [ ( 2 4 4 2 6 24 ) ( 0 4 4 0 6 24 ) ] = 2 π [ 4 8 3 ] = 2 π ( 4 3 ) = 8 π 3
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Aleah Booth
Answered 2022-07-29 Author has 5 answers
2 π 0 2  ( y 3 2 y 5 4 + y 3 2 ) d y = 2 π 0 2 y 5 4 d y
= 2 π [ y 6 24 ] 0 2 = 2 π ( 64 24 0 ) = 16 π 3
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