What is the integral from 0 to 1 of ax+bx^3 ?

The integral from 0 to 1 of ax+bx^3 is a/2+b/4

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integral from 0 to 1 of ax+bx^3

\int_{0}^{1} a x + b x^{3} d x

\frac{a}{2} + \frac{b}{4}

Solution steps

\int_{0}^{1} a x + b x^{3} 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}^{1} a x d x + \int_{0}^{1} b x^{3} d x

\int_{0}^{1} a x d x = \frac{a}{2}

\int_{0}^{1} b x^{3} d x = \frac{b}{4}

= \frac{a}{2} + \frac{b}{4}

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What is the integral from 0 to 1 of ax+bx^3 ?
The integral from 0 to 1 of ax+bx^3 is a/2+b/4