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underset(-pi/2)overset(pi/2)intsin^(7)xd...

`underset(-pi/2)overset(pi/2)intsin^(7)xdx`

Text Solution

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`int_(-pi//2)^(pi//2) sin^(7) x dx`
`" Let " f(x) =sin^(7) x`
`f(-x)=sin^(7)(-x)=[-sinx]^(7)=-sin^(7)x`
`rArr f(x)` is an odd function
`int_(-pi//2)^(pi//2) sin^(7) x dx =0`
`[ :' int_(-a)^(a) f(x) dx=0 " if " f(x) " is an odd fucntion"]`
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