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प्रश्न
Evaluate the following:
`int_1^0 x^2 (1 - x)^3 "d"x`
उत्तर
By applying reduction formula
`int_0^1 x^"m" (1 - x)^"n" "d"x = ("m"! xx "n"!)/(("m" + "n" + 1)!)`
`int_0^1 x^"m" (1 - x)^"n" "d"x = (2! xx 3!)/(6!)`
= `(2 xx 1 xx 3 xx 2 xx 1)/(6 xx 5 xx 4 xx 3 xx 2 xx 1)`
`int_0^1 x^"m" (1 - x)^"n" "d"x = 1/60`
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