Integrate : $\int \limits_0^{\frac{\pi}{2}} \sin^{\frac{3}{4}} \cos ^3 x dx$

Question

$$\begin {array} {1 1} (a)\;\frac{4}{105} \\ (b)\;\frac{16}{105} \\ (c)\;\frac{32}{105} \\ (d)\;\frac{64}{105} \end {array}$$