What is the integral from 0 to 3 of pi(4x^2)^2 ?

The integral from 0 to 3 of pi(4x^2)^2 is (3888pi)/5

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integral from 0 to 3 of pi(4x^2)^2

\int_{0}^{3} π (4 x^{2})^{2} d x

\frac{3888 π}{5}

Decimal

2442.90244 \dots

Solution steps

\int_{0}^{3} π (4 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} (4 x^{2})^{2} d x

Simplify

(4 x^{2})^{2} : 16 x^{4}

= π \cdot \int_{0}^{3} 16 x^{4} d x

Take the constant out:

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

= π 16 \cdot \int_{0}^{3} x^{4} d x

Apply the Power Rule

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

= π 16 [\frac{x ^{5}}{5}]_{0}^{3}

Compute the boundaries:

\frac{243}{5}

= π 16 \cdot \frac{243}{5}

Simplify

= \frac{3888 π}{5}

\int_{0}^{1} 4 - x^{2} d x

\int_{0}^{3} x (9 - x^{2}) d x

\int_{0}^{e} \frac{1 + ln ( x )}{x} d x

\int_{4}^{9} \frac{2 + x}{2 x} d x

\int_{0}^{5} s 25 - s^{2} d s

What is the integral from 0 to 3 of pi(4x^2)^2 ?
The integral from 0 to 3 of pi(4x^2)^2 is (3888pi)/5