What is the integral from-2 to 0 of (x^2y-2xy) ?

The integral from-2 to 0 of (x^2y-2xy) is -2x^2+4x

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integral from-2 to 0 of (x^2y-2xy)

\int_{- 2}^{0} (x^{2} y - 2 x y) d y

- 2 x^{2} + 4 x

Solution steps

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

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

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

= - 2 x^{2} - (- 4 x)

Simplify

= - 2 x^{2} + 4 x

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What is the integral from-2 to 0 of (x^2y-2xy) ?
The integral from-2 to 0 of (x^2y-2xy) is -2x^2+4x