What is the integral from 0 to 1 of pi(3x)^2 ?

The integral from 0 to 1 of pi(3x)^2 is 3pi

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integral from 0 to 1 of pi(3x)^2

\int_{0}^{1} π (3 x)^{2} d x

3 π

Decimal

9.42477 \dots

Solution steps

\int_{0}^{1} π (3 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} (3 x)^{2} d x

Simplify

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

= π \cdot \int_{0}^{1} 9 x^{2} 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}^{1} x^{2} d x

Apply the Power Rule

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

= π 9 [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= π 9 \cdot \frac{1}{3}

Simplify

= 3 π

\frac{d}{d x} (7^{x})

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 4 + e^{\frac{x}{2}}

n = 1 \sum \infty \frac{( 4 ^{n} + 1 )}{5 ^{n}}

\int - x e^{- 2 x} d x

5 - x^{2}

What is the integral from 0 to 1 of pi(3x)^2 ?
The integral from 0 to 1 of pi(3x)^2 is 3pi