What is the integral from-1 to 2 of (2x^2+5x^3y) ?

The integral from-1 to 2 of (2x^2+5x^3y) is 6x^2+(15x^3)/2

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integral from-1 to 2 of (2x^2+5x^3y)

\int_{- 1}^{2} (2 x^{2} + 5 x^{3} y) d y

6 x^{2} + \frac{15 x ^{3}}{2}

Solution steps

\int_{- 1}^{2} 2 x^{2} + 5 x^{3} 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_{- 1}^{2} 2 x^{2} d y + \int_{- 1}^{2} 5 x^{3} y d y

\int_{- 1}^{2} 2 x^{2} d y = 6 x^{2}

\int_{- 1}^{2} 5 x^{3} y d y = \frac{15 x ^{3}}{2}

= 6 x^{2} + \frac{15 x ^{3}}{2}

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What is the integral from-1 to 2 of (2x^2+5x^3y) ?
The integral from-1 to 2 of (2x^2+5x^3y) is 6x^2+(15x^3)/2