Provide an Appropriate Response $\int _ { 0 } ^ { \infty } \frac { 4 x ^ { 3 } } { x ^ { 4 } + 1 } d x$

question 369

Essay

Provide an appropriate response.
-i) Show that $\int _ { 0 } ^ { \infty } \frac { 4 x ^ { 3 } } { x ^ { 4 } + 1 } d x$ diverges, and hence $\int _ { - \infty } ^ { \infty } \frac { 4 x ^ { 3 } } { x ^ { 4 } + 1 } d x$ diverges.
ii) Show that $\lim _ { b \rightarrow \infty } \int _ { - b } ^ { b } \frac { 4 x ^ { 3 } } { x ^ { 4 } + 1 } d x = 0$ .

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