What is the integral from 0 to 1 of (x+1)sqrt(1-x) ?

The integral from 0 to 1 of (x+1)sqrt(1-x) is 14/15

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integral from 0 to 1 of (x+1)sqrt(1-x)

\int_{0}^{1} (x + 1) 1 - x d x

\frac{14}{15}

Decimal

0.93333 \dots

Solution steps

\int_{0}^{1} (x + 1) 1 - x d x

Apply Integration By Parts

= [- \frac{2}{3} (x + 1) (1 - x)^{\frac{3}{2}} - \int - \frac{2}{3} (1 - x)^{\frac{3}{2}} d x]_{0}^{1}

\int - \frac{2}{3} (1 - x)^{\frac{3}{2}} d x = \frac{4}{15} (1 - x)^{\frac{5}{2}}

= [- \frac{2}{3} (x + 1) (1 - x)^{\frac{3}{2}} - \frac{4}{15} (1 - x)^{\frac{5}{2}}]_{0}^{1}

Compute the boundaries:

\frac{14}{15}

= \frac{14}{15}

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What is the integral from 0 to 1 of (x+1)sqrt(1-x) ?
The integral from 0 to 1 of (x+1)sqrt(1-x) is 14/15