Use Series to Approximate the Definite Integral to Within the Indicated

Multiple Choice

Use series to approximate the definite integral to within the indicated accuracy.
$$\int _ { 0 } ^ { 0.5 } x ^ { 2 } e ^ { - x ^ { 2 } } d x \quad | e r r o r | < 0.001$$

A) $0.0354$
B) $0.0125$
C) $0.0625$
D) $0.1447$
E) $0.2774$