What is the integral from 0 to 1 of 0.5e^{x^2} ?

The integral from 0 to 1 of 0.5e^{x^2} is 0.44311…\erfi(1)

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integral from 0 to 1 of 0.5e^{x^2}

\int_{0}^{1} 0.5 e^{x^{2}} d x

0.44311 \dots erfi (1)

Solution steps

\int_{0}^{1} 0.5 e^{x^{2}} d x

Take the constant out:

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

= 0.5 \cdot \int_{0}^{1} e^{x^{2}} d x

Use the nonelementary integral:

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

= 0.5 [\frac{π}{2} erfi (x)]_{0}^{1}

Simplify

= 0.5 [0.88622 \dots erfi (x)]_{0}^{1}

Compute the boundaries:

0.88622 \dots erfi (1)

= 0.5 \cdot 0.88622 \dots erfi (1)

Simplify

= 0.44311 \dots erfi (1)

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What is the integral from 0 to 1 of 0.5e^{x^2} ?
The integral from 0 to 1 of 0.5e^{x^2} is 0.44311…\erfi(1)