What is the integral from 0 to 2 of ax^2+bx ?

The integral from 0 to 2 of ax^2+bx is (8a)/3+b*2

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integral from 0 to 2 of ax^2+bx

\int_{0}^{2} a x^{2} + b x d x

\frac{8 a}{3} + b \cdot 2

Solution steps

\int_{0}^{2} a x^{2} + b x 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} a x^{2} d x + \int_{0}^{2} b x d x

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

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

= \frac{8 a}{3} + b \cdot 2

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What is the integral from 0 to 2 of ax^2+bx ?
The integral from 0 to 2 of ax^2+bx is (8a)/3+b*2