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

Popular >

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}

= [- \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}

\int_{1}^{2} (- x^{2} + x + 2) d x

\int_{- 1}^{1} x 1 + x^{2} d x

\int_{0}^{π} (x cos (x)) d x

\int_{0}^{1} x^{3} 4 x^{2} + 1 d x

\int_{0}^{5 π} sin (x) d x

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