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

The integral from 0 to 2 of pi(3x^2)^2 is (288pi)/5

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

\int_{0}^{2} π (3 x^{2})^{2} d x

\frac{288 π}{5}

Decimal

180.95573 \dots

Solution steps

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

Simplify

(3 x^{2})^{2} : 9 x^{4}

= π \cdot \int_{0}^{2} 9 x^{4} d x

Take the constant out:

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

= π 9 \cdot \int_{0}^{2} x^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{0}^{2}

= π 9 [\frac{x ^{5}}{5}]_{0}^{2}

Compute the boundaries:

\frac{32}{5}

= π 9 \cdot \frac{32}{5}

Simplify

= \frac{288 π}{5}

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{4})

x \to 1 - lim (\frac{1}{x} - 1)

y^{^{''}} + 9 y = 3 sec (3 t)

f (x) = cos (x^{2}) \cdot 2 x

y = x + 1, y = 9 - x^{2}, x = - 1, x = 2

What is the integral from 0 to 2 of pi(3x^2)^2 ?
The integral from 0 to 2 of pi(3x^2)^2 is (288pi)/5