What is the integral from 0 to 10-2z of 12y-8x ?

The integral from 0 to 10-2z of 12y-8x is 6(-2z+10)^2-8x(-2z+10)

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integral from 0 to 10-2z of 12y-8x

\int_{0}^{10 - 2 z} 12 y - 8 x d y

6 (- 2 z + 10)^{2} - 8 x (- 2 z + 10)

Solution steps

\int_{0}^{10 - 2 z} 12 y - 8 x d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{10 - 2 z} 12 y d y - \int_{0}^{10 - 2 z} 8 x d y

\int_{0}^{10 - 2 z} 12 y d y = 6 (- 2 z + 10)^{2}

\int_{0}^{10 - 2 z} 8 x d y = 8 x (- 2 z + 10)

= 6 (- 2 z + 10)^{2} - 8 x (- 2 z + 10)

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What is the integral from 0 to 10-2z of 12y-8x ?
The integral from 0 to 10-2z of 12y-8x is 6(-2z+10)^2-8x(-2z+10)