What is the integral from 0.4 to 1 of x(1-x)^8 ?

The integral from 0.4 to 1 of x(1-x)^8 is 0.00051…

Popular >

integral from 0.4 to 1 of x(1-x)^8

\int_{0.4}^{1} x (1 - x)^{8} d x

0.00051 \dots

Solution steps

\int_{0.4}^{1} x (1 - x)^{8} d x

Apply Integration By Parts

: [- 0.11111 \dots x (1 - x)^{9} - \int - \frac{1}{9} (1 - x)^{9} d x]_{0.4}^{1}

= [- 0.11111 \dots x (1 - x)^{9} - \int - \frac{1}{9} (1 - x)^{9} d x]_{0.4}^{1}

\int - \frac{1}{9} (1 - x)^{9} d x = \frac{1}{90} (1 - x)^{10}

= [- 0.11111 \dots x (1 - x)^{9} - \frac{1}{90} (1 - x)^{10}]_{0.4}^{1}

Simplify

= [- 0.11111 \dots x (1 - x)^{9} - 0.01111 \dots (1 - x)^{10}]_{0.4}^{1}

Compute the boundaries:

0.00051 \dots

= 0.00051 \dots

\int_{1}^{3} (3 x^{2} - x) d x

\int_{1}^{4} e^{- x} x - e^{- x} d x

\int_{- 42.25}^{0} (\frac{13}{2} x)^{2} d x

\int_{0}^{x} \frac{1}{( 1 - x ) ^{\frac{2}{3}}} d x

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

What is the integral from 0.4 to 1 of x(1-x)^8 ?
The integral from 0.4 to 1 of x(1-x)^8 is 0.00051…