What is the integral from 0 to 9 of 2piy(y/3) ?

The integral from 0 to 9 of 2piy(y/3) is 162pi

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integral from 0 to 9 of 2piy(y/3)

\int_{0}^{9} 2 π y (\frac{y}{3}) d y

162 π

Decimal Notation

508.93800 \dots

Solution steps

\int_{0}^{9} 2 π y \frac{y}{3} d y

Take the constant out:

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

= 2 π \frac{1}{3} \cdot \int_{0}^{9} yy d y

2 π \frac{1}{3} = \frac{2 π}{3}

= \frac{2 π}{3} \cdot \int_{0}^{9} yy d y

Simplify

yy : y^{2}

= \frac{2 π}{3} \cdot \int_{0}^{9} y^{2} d y

Apply the Power Rule

: [\frac{y ^{3}}{3}]_{0}^{9}

= \frac{2 π}{3} [\frac{y ^{3}}{3}]_{0}^{9}

Compute the boundaries:

243

= \frac{2 π}{3} \cdot 243

Simplify

= 162 π

e^{\frac{x}{x - 4}}

\frac{8 s + 2}{s ^{2} - 25}

\frac{d y}{d x} + x^{2} y = x^{2}

n = 1 \sum \infty \frac{4}{7 ^{n}} + \frac{3}{n}

(2 x y^{2} - 7) d x + (2 x^{2} y + 6) d y = 0

What is the integral from 0 to 9 of 2piy(y/3) ?
The integral from 0 to 9 of 2piy(y/3) is 162pi