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Evaluate : int x " sin"^(3) x^(2) ." cos...

Evaluate : `int x " sin"^(3) x^(2) ." cos "x^(2) dx`

Text Solution

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`"Let I " =int x" sin"^(3) x^(2)."cos" x^(2)dx`
`=int("sin x"^(2))^(3)."(x cos x"^(2)") dx"`
`"Let sin"x^(2) =t`
`rArr " "2x."cos"x^(2)=(dt)/(dx)`
`rArr " "x"cos "x^(2) dx =(dt)/(2)`
`"Now "" "I=int t^(3) .(dt)/(2) =1/8 t^(4)+c`
`=1/8"sin"^(4)x^(2)+c.`
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