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

The integral from 0 to 3 of pi(x^2)^2 is (243pi)/5

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

\int_{0}^{3} π (x^{2})^{2} d x

\frac{243 π}{5}

Decimal

152.68140 \dots

Solution steps

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

Simplify

(x^{2})^{2} : x^{4}

= π \cdot \int_{0}^{3} x^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{0}^{3}

= π [\frac{x ^{5}}{5}]_{0}^{3}

Compute the boundaries:

\frac{243}{5}

= π \frac{243}{5}

Simplify

= \frac{243 π}{5}

\int_{3}^{7} (1 + 2 x) d x

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

\int_{- 2}^{3} x + 3 d x

\int_{0}^{1} x 2 - x^{2} - x^{3} d x

\int_{1}^{3} (5 x^{2}) d x

What is the integral from 0 to 3 of pi(x^2)^2 ?
The integral from 0 to 3 of pi(x^2)^2 is (243pi)/5