Use series to approximate the definite integral to within the indicated accuracy. $\int _ { 0 } ^ { 05 } x ^ { 2 } e ^ { - x ^ { 2 } } d x \quad \mid \text { error } \mid

Question

Use series to approximate the definite integral to within the indicated accuracy. $\int _ { 0 } ^ { 05 } x ^ { 2 } e ^ { - x ^ { 2 } } d x \quad \mid \text { error } \mid < 0.001$
A) 0.0354
B) 0.0125
C) 0.0625
D) 0.1447
E) 0.2774

Quizplus · Accepted Answer

The integral can be approximated using the series expansion of $e^{-x^2}$. The series converges quickly, and calculating a few terms gives an approximation of 0.0354, which satisfies the error condition.

Use Series to Approximate the Definite Integral to Within the Indicated