What is the integral from 0 to 1 of 7e^{x^2} ?

The integral from 0 to 1 of 7e^{x^2} is (7sqrt(pi))/2 \erfi(1)

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integral from 0 to 1 of 7e^{x^2}

\int_{0}^{1} 7 e^{x^{2}} d x

\frac{7 π}{2} erfi (1)

Solution steps

\int_{0}^{1} 7 e^{x^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int_{0}^{1} e^{x^{2}} d x

Use the nonelementary integral:

\int e^{x^{2}} d x = \frac{π}{2} erfi (x)

= 7 [\frac{π}{2} erfi (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{2} erfi (1)

= 7 \cdot \frac{π}{2} erfi (1)

Simplify

= \frac{7 π}{2} erfi (1)

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What is the integral from 0 to 1 of 7e^{x^2} ?
The integral from 0 to 1 of 7e^{x^2} is (7sqrt(pi))/2 \erfi(1)