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Evaluate the following integrals: in...

Evaluate the following integrals: `int_(-1)^1|xcospix|dx`

Text Solution

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`int_(-1)^1|xcospix|dx` f(-x)=|(-x)cospi(-x)|dx f(-x)=f(x)
So,
I=2`int_0^1|xcospix|dx` I=2[`int_0^(1/2)|xcospix|dx`+`int_(1/2)^1xcospi(-x)dx`]
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