What is the integral from 1 to 2 of x(2-x)^{99} ?

The integral from 1 to 2 of x(2-x)^{99} is 51/5050

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integral from 1 to 2 of x(2-x)^{99}

\int_{1}^{2} x (2 - x)^{99} d x

\frac{51}{5050}

Decimal

0.01009 \dots

Solution steps

\int_{1}^{2} x (2 - x)^{99} d x

Apply Integration By Parts

: [- \frac{1}{100} x (2 - x)^{100} - \int - \frac{1}{100} (2 - x)^{100} d x]_{1}^{2}

= [- \frac{1}{100} x (2 - x)^{100} - \int - \frac{1}{100} (2 - x)^{100} d x]_{1}^{2}

\int - \frac{1}{100} (2 - x)^{100} d x = \frac{1}{10100} (2 - x)^{101}

= [- \frac{1}{100} x (2 - x)^{100} - \frac{1}{10100} (2 - x)^{101}]_{1}^{2}

Simplify

[- \frac{1}{100} x (2 - x)^{100} - \frac{1}{10100} (2 - x)^{101}]_{1}^{2} : [- \frac{1}{5050} (- x + 2)^{100} (50 x + 1)]_{1}^{2}

= [- \frac{1}{5050} (- x + 2)^{100} (50 x + 1)]_{1}^{2}

Compute the boundaries:

\frac{51}{5050}

= \frac{51}{5050}

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What is the integral from 1 to 2 of x(2-x)^{99} ?
The integral from 1 to 2 of x(2-x)^{99} is 51/5050