What is the integral from 2 to y/2 of 6x^2y ?

The integral from 2 to y/2 of 6x^2y is 6y((y^3)/(24)-8/3)

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integral from 2 to y/2 of 6x^2y

\int_{2}^{\frac{y}{2}} 6 x^{2} y d x

6 y (\frac{y ^{3}}{24} - \frac{8}{3})

Solution steps

\int_{2}^{\frac{y}{2}} 6 x^{2} y d x

Take the constant out:

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

= 6 y \cdot \int_{2}^{\frac{y}{2}} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{2}^{\frac{y}{2}}

= 6 y [\frac{x ^{3}}{3}]_{2}^{\frac{y}{2}}

Compute the boundaries:

\frac{y ^{3}}{24} - \frac{8}{3}

= 6 y (\frac{y ^{3}}{24} - \frac{8}{3})

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What is the integral from 2 to y/2 of 6x^2y ?
The integral from 2 to y/2 of 6x^2y is 6y((y^3)/(24)-8/3)