Find an infinite series that converges to the value of $\int _ { 0 } ^ { 1 } x ^ { 2 } e ^ { - x ^ { 3 } }$ dx. Is $\frac { 1 } { 3 } - \frac { 1 } { 6 } + \frac { 1 } { 18 } - \frac { 1 } { 72 } \ldots$ correct?

Name: Find an infinite series that converges to the value of $\int _ { 0 } ^ { 1 } x ^ { 2 } e ^ { - x ^ { 3 } }$ dx. Is $\frac { 1 } { 3 } - \frac { 1 } { 6 } + \frac { 1 } { 18 } - \frac { 1 } { 72 } \ldots$ correct?
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Question

Find an infinite series that converges to the value of

\int _ { 0 } ^ { 1 } x ^ { 2 } e ^ { - x ^ { 3 } }

dx. Is

\frac { 1 } { 3 } - \frac { 1 } { 6 } + \frac { 1 } { 18 } - \frac { 1 } { 72 } \ldots

correct?

Quizplus · Accepted Answer

The given series is the Taylor series expansion of the integrand, which converges to the value of the integral.

Find an Infinite Series That Converges to the Value Of \int