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

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

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

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

6 x^{2} (\frac{x ^{2}}{8} - 2)

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{x ^{2}}{8} - 2

= 6 x^{2} (\frac{x ^{2}}{8} - 2)

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