What is the integral from 0 to 1 of (x-0.5)^2 ?

The integral from 0 to 1 of (x-0.5)^2 is 0.08333…

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integral from 0 to 1 of (x-0.5)^2

\int_{0}^{1} (x - 0.5)^{2} d x

0.08333 \dots

Solution steps

\int_{0}^{1} (x - 0.5)^{2} d x

Apply u-substitution

: \int_{- 0.5}^{0.5} u^{2} d u

= \int_{- 0.5}^{0.5} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{- 0.5}^{0.5}

= [\frac{u ^{3}}{3}]_{- 0.5}^{0.5}

Simplify

= [0.33333 \dots u^{3}]_{- 0.5}^{0.5}

Compute the boundaries:

0.08333 \dots

= 0.08333 \dots

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What is the integral from 0 to 1 of (x-0.5)^2 ?
The integral from 0 to 1 of (x-0.5)^2 is 0.08333…