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प्रश्न
Evaluate the following:
`int_0^(pi/2) sin^10 x "d"x`
उत्तर
Here n = 10, which is even
∴ `int_0^(pi/2) sin^"n" x "d"x = (("n" - 1))/"n" xx (("n" - 3))/(("n" - 2)) xx ...... xx 1/2 xx pi/2`
`int_0^(pi/2) sin^10 x "d"x = 9/10 xx 7/8 xx 5/6 xx 3/4 xx 1/2 xx pi/2`
= `(63pi)/512`
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