What is the integral from 0 to 1 of pix^2 ?

The integral from 0 to 1 of pix^2 is pi/3

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integral from 0 to 1 of pix^2

\int_{0}^{1} π x^{2} d x

\frac{π}{3}

Decimal

1.04719 \dots

Solution steps

\int_{0}^{1} π x^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{0}^{1} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{1}

= π [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= π \frac{1}{3}

Simplify

= \frac{π}{3}

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What is the integral from 0 to 1 of pix^2 ?
The integral from 0 to 1 of pix^2 is pi/3