What is the integral from 0 to 2 of pi(x^3)^2 ?

The integral from 0 to 2 of pi(x^3)^2 is (128pi)/7

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integral from 0 to 2 of pi(x^3)^2

\int_{0}^{2} π (x^{3})^{2} d x

\frac{128 π}{7}

Decimal

57.44626 \dots

Solution steps

\int_{0}^{2} π (x^{3})^{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}^{2} (x^{3})^{2} d x

Simplify

(x^{3})^{2} : x^{6}

= π \cdot \int_{0}^{2} x^{6} d x

Apply the Power Rule

: [\frac{x ^{7}}{7}]_{0}^{2}

= π [\frac{x ^{7}}{7}]_{0}^{2}

Compute the boundaries:

\frac{128}{7}

= π \frac{128}{7}

Simplify

= \frac{128 π}{7}

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What is the integral from 0 to 2 of pi(x^3)^2 ?
The integral from 0 to 2 of pi(x^3)^2 is (128pi)/7