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प्रश्न
Evaluate the following:
`int_0^(pi/2) cos^7 x "d"x`
उत्तर
Here n = 7, which is odd
∴ `int_0^(pi/2) cos^"n" x "d"x = (("" - 1))/"n" xx (("n" - 3))/(("n" - 2)) xx ...... xx 2/3`
`int_0^(pi/2) cos^7 x "d"x = 6/7 xx 4/5 xx 2/3 xx 1`
= `16/35`
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