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Evaluate int_(-pi//4)^(pi//4)x^(3)sin^(2)xdx

Answer»

SOLUTION :`:'f(x)=x^(3)SIN^(2)x`
Now, `f(-x)=(-x)^(3)sin^(2)(-x)=-x^(3)sin^(2)x=-f(x)` (odd function)
`:. Int_(-pi//4)^(pi//4)x^(3)sin^(2)xdx=0`


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