Evaluate the Following Integrals:
(A) $\int _ { 0 } ^ { x / 2 } \sin ^ { 4 } x \cos x d x$

Essay

Evaluate the following integrals:
(a) $\int _ { 0 } ^ { x / 2 } \sin ^ { 4 } x \cos x d x$ (b) $\int _ { 0 } ^ { \pi / 2 } \sin ^ { 4 } x \cos ^ { 3 } x d x$ (c) $\int _ { 0 } ^ { x / 4 } \sin 2 x \cos ^ { 4 } 2 x d x$ (d) $\int _ { 0 } ^ { x } \cos ^ { 4 } x d x$