The improper integral ${\displaystyle \underset{0}{\overset{}{}}}f(x)dx$ cannot be converted into an integral with finite limits using the substitution $t=\frac{1}{x}$ because the limit at zero becomes infinite. The problem is resolved by first writing ${\displaystyle \underset{0}{\overset{}{}}}f(x)dx={\displaystyle \underset{0}{\overset{1}{}}}f(x)dx{\displaystyle \underset{1}{\overset{}{}}}f(x)dx.$ Apply this technique to approximate the following improper integrals to within ${10}^{-6}.$

a$.{\displaystyle \underset{0}{\overset{}{}}}\frac{1}{1x^4}dx$

b$.{\displaystyle \underset{0}{\overset{}{}}}\frac{1}{(1x^2{)}^3}dx$