What is the integral from 0 to 2 of (2x^2y+5y^4) ?

The integral from 0 to 2 of (2x^2y+5y^4) is 10y^4+(16y)/3

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integral from 0 to 2 of (2x^2y+5y^4)

\int_{0}^{2} (2 x^{2} y + 5 y^{4}) d x

10 y^{4} + \frac{16 y}{3}

Solution steps

\int_{0}^{2} 2 x^{2} y + 5 y^{4} d x

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} 5 y^{4} d x + \int_{0}^{2} 2 y x^{2} d x

\int_{0}^{2} 5 y^{4} d x = 10 y^{4}

\int_{0}^{2} 2 y x^{2} d x = \frac{16 y}{3}

= 10 y^{4} + \frac{16 y}{3}

What is the integral from 0 to 2 of (2x^2y+5y^4) ?
The integral from 0 to 2 of (2x^2y+5y^4) is 10y^4+(16y)/3