What is the integral from 0 to 1 of e^xsqrt(1-x) ?

The integral from 0 to 1 of e^xsqrt(1-x) is 1.03007…

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integral from 0 to 1 of e^xsqrt(1-x)

\int_{0}^{1} e^{x} 1 - x d x

1.03007 \dots

Solution steps

\int_{0}^{1} e^{x} 1 - x d x

Apply Integration By Parts

= [e^{x} 1 - x - \int - \frac{e ^{x}}{2 1 - x} d x]_{0}^{1}

\int - \frac{e ^{x}}{2 1 - x} d x = \frac{e π}{2} erf (1 - x)

= [e^{x} 1 - x - \frac{e π}{2} erf (1 - x)]_{0}^{1}

Compute the boundaries:

1.03007 \dots

= 1.03007 \dots

What is the integral from 0 to 1 of e^xsqrt(1-x) ?
The integral from 0 to 1 of e^xsqrt(1-x) is 1.03007…