Using the first three nonzero terms of the Maclaurin series, the approximated value of $\int _ { 0 } ^ { 1 } e ^ { x ^ { 2 } } d x$ is

A) $\frac { 53 } { 30 }$
B) $\frac { 43 } { 30 }$
C) $\frac { 41 } { 30 }$
D) $\frac { 37 } { 30 }$
E) $\frac { 31 } { 30 }$

Question

Using the first three nonzero terms of the Maclaurin series, the approximated value of $\int _ { 0 } ^ { 1 } e ^ { x ^ { 2 } } d x$ is

A) $\frac { 53 } { 30 }$
B) $\frac { 43 } { 30 }$
C) $\frac { 41 } { 30 }$
D) $\frac { 37 } { 30 }$
E) $\frac { 31 } { 30 }$

Quizplus · Accepted Answer

The Maclaurin series for $e^{x^2}$ starts with $1 + x^2 + \frac{x^4}{2!} + \cdots$. Integrating each term from 0 to 1 gives $\int_0^1 (1 + x^2 + \frac{x^4}{2}) dx = [x + \frac{x^3}{3} + \frac{x^5}{10}]_0^1 = 1 + \frac{1}{3} + \frac{1}{10} = \frac{30}{30} + \frac{10}{30} + \frac{3}{30} = \frac{43}{30}$.

Using the First Three Nonzero Terms of the Maclaurin Series ∫01ex2dx\int _ { 0 } ^ { 1 } e ^ { x ^ { 2 } } d x∫01​ex2dx

Using the First Three Nonzero Terms of the Maclaurin Series $\int _ { 0 } ^ { 1 } e ^ { x ^ { 2 } } d x$