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Popular >

integral from 0 to 1 of x(1-x)^8

Solution

\int_{0}^{1} x (1 - x)^{8} d x

Solution

\frac{1}{90}

+1

Decimal Notation

0.01111 \dots

Solution steps

\int_{0}^{1} x (1 - x)^{8} d x

Apply Integration By Parts

: [- \frac{1}{9} x (1 - x)^{9} - \int - \frac{1}{9} (1 - x)^{9} d x]_{0}^{1}

= [- \frac{1}{9} x (1 - x)^{9} - \int - \frac{1}{9} (1 - x)^{9} d x]_{0}^{1}

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

= [- \frac{1}{9} x (1 - x)^{9} - \frac{1}{90} (1 - x)^{10}]_{0}^{1}

Compute the boundaries:

\frac{1}{90}

= \frac{1}{90}

Popular Examples

area f(x)=sin(x),0, pi/2 area

f (x) = sin (x), 0, \frac{π}{2}

derivative of xe^{5y}

\frac{d}{d x} (x e^{5 y})

tangent of y=(4x)/(x+3),(1,1)tangent of

y = \frac{4 x}{x + 3}, (1, 1)

integral of x^2e^{x^{3+4}}

\int x^{2} e^{x^{3 + 4}} d x

tangent of f(x)=log_{2}(2x^2+14),\at x=5 tangent of

f (x) = lo g_{2} (2 x^{2} + 14), at x = 5

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x(1-x)^8 ?
The integral from 0 to 1 of x(1-x)^8 is 1/90