Determine Whether Each Integral Is Convergent or Divergent $\int _ { 1 } ^ { \infty } x ^ { - 5 / 4 } d x$

Essay

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.(a) $\int _ { 1 } ^ { \infty } x ^ { - 5 / 4 } d x$ (b) $\int _ { - \infty } ^ { 1 } \frac { 1 } { \sqrt { x } } d x$ (c) $\int _ { 0 } ^ { \infty } x e ^ { - 2 x } d x$