What is the integral from 0 to 2 of x+3x^2y^2 ?

The integral from 0 to 2 of x+3x^2y^2 is 2+8y^2

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integral from 0 to 2 of x+3x^2y^2

\int_{0}^{2} x + 3 x^{2} y^{2} d x

2 + 8 y^{2}

Solution steps

\int_{0}^{2} x + 3 x^{2} y^{2} 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} x d x + \int_{0}^{2} 3 y^{2} x^{2} d x

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

\int_{0}^{2} 3 y^{2} x^{2} d x = 8 y^{2}

= 2 + 8 y^{2}

\int_{- 1}^{2} x^{2} + 1 - x d x

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\int_{1}^{4} ∣ 2 x - 4 ∣ d x

What is the integral from 0 to 2 of x+3x^2y^2 ?
The integral from 0 to 2 of x+3x^2y^2 is 2+8y^2