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int- 1^1x^(17)cos^4x dx=0...

`int_- 1^1x^(17)cos^4x dx=0`

Text Solution

Verified by Experts

`" Let " f(x) =x^(17) cos^(14) x`
`rArr" " f(-x) =(-x)^(17) cos^(4) (-x)`
`=-(x)^(17)cos^(4)x=-f(x)`
Therfore f(x) is an odd function .
we know that if f(x) is an odd function then
`int_(-a)^(a) f(x) dx=0`
`:. int_(-1)^(1) x^(17) cos^(4) x dx=0`
Hence proved
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