12. Techniques of Integration

Given that the definite integral from $0$ to $\pi$ of ${\sin }^4\left(x\right)dx$ equals $\frac{3}{8\pi }$, what is the value of the definite integral from $0$ to $\pi$ of ${\cos }^4\left(x\right)dx$?

If n is a known positive integer, for what value of k does the following hold: ${\int }_{}^{}k{x}^{n-1}dx$ = $\frac{1}{n}$?