What is the integral from 0 to 2 of 6x^2y-2x ?

The integral from 0 to 2 of 6x^2y-2x is -4x+12x^2

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integral from 0 to 2 of 6x^2y-2x

\int_{0}^{2} 6 x^{2} y - 2 x d y

- 4 x + 12 x^{2}

Solution steps

\int_{0}^{2} 6 x^{2} y - 2 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}^{2} 2 x d y + \int_{0}^{2} 6 x^{2} y d y

\int_{0}^{2} 2 x d y = 4 x

\int_{0}^{2} 6 x^{2} y d y = 12 x^{2}

= - 4 x + 12 x^{2}

What is the integral from 0 to 2 of 6x^2y-2x ?
The integral from 0 to 2 of 6x^2y-2x is -4x+12x^2