$\text { Use integration tables to evaluate the integral } \int _ { 0 } ^ { 1 } x ^ { 9 } e ^ { x ^ { 10 } } d x \text {. }$
A) $\frac { 1 } { 10 } \left( e ^ { 10 } - e \right)$
B) $e ^ { 10 } - 1$
C) $\frac { 1 } { 10 } ( e - 1 )$
D) $e ^ { 10 } - e$
E) $10 ( e - 1 )$

Question

$\text { Use integration tables to evaluate the integral } \int _ { 0 } ^ { 1 } x ^ { 9 } e ^ { x ^ { 10 } } d x \text {. }$ 
A) $\frac { 1 } { 10 } \left( e ^ { 10 } - e \right)$
B) $e ^ { 10 } - 1$
C) $\frac { 1 } { 10 } ( e - 1 )$
D) $e ^ { 10 } - e$
E) $10 ( e - 1 )$

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = x^{10} $, then $ du = 10x^9 dx $. The limits change from 0 to 1 for $ x $ to 0 to 1 for $ u $. The integral becomes $\frac{1}{10} \int_0^1 e^u du = \frac{1}{10} (e - 1)$.

Use integration tables to evaluate the integral ∫01x9ex10dx. \text { Use integration tables to evaluate the integral } \int _ { 0 } ^ { 1 } x ^ { 9 } e ^ { x ^ { 10 } } d x \text {. } Use integration tables to evaluate the integral ∫01​x9ex10dx.

$\text { Use integration tables to evaluate the integral } \int _ { 0 } ^ { 1 } x ^ { 9 } e ^ { x ^ { 10 } } d x \text {. }$