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

Options

A. `(3pi)/(216)`
B. `(3pi)/(512)`
C. `(pi)/(512)`
D. none of these

Explanation

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)`