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AP® Calculus AB-BC

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Difficult

Approximate an Integral Using a Series

APCALC-HJWJ1G

Find the first three non-zero terms of a power series for ${ e }^{ { x }^{ 2 } }$ centered at $0$ and use them to estimate the given integral $\int _{ 0 }^{ 1 }{ { e }^{ { x }^{ 2 } } } dx$.

A

$1+e+\frac { 1 }{ 2 } { e }^{ 2 }$

B

$1+1+\frac { 1 }{ 2 } $

C

$0+2+2$

D

$1+\frac { 1 }{ 3 } +\frac { 1 }{ 10 } $