1.

The value of int_(0)^(pi//2) sin^(4)x cos^(6)x dx, is

Answer»

`(3pi)/(216)`
`(3pi)/(512)`
`(pi)/(512)`
none of these

Solution :Using Gamma Function, we have
`underset(0)overset(pi//2)int sin^(4)x cos^(6)x dx=(Gamma(5//2)Gamma(7//2))/(2Gamma(4+6+2)/(2))=(Gamma(5//2)Gamma(7//2))/(2Gamma6)`
`rArr `underset(0)overset(pi//2)int sin^(4)x cos^(6)x dx=(((3)/(2)XX(1)/(2)xxGamma(1)/(2))((5)/(2)xx(3)/(2)xx(1)/(2)xxGamma(1)/(2)))/(2xx5!)=(3pi)/(512)`


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