What is the integral from 0 to 1 of ax^3+bx^4 ?

The integral from 0 to 1 of ax^3+bx^4 is a/4+b/5

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integral from 0 to 1 of ax^3+bx^4

\int_{0}^{1} a x^{3} + b x^{4} d x

\frac{a}{4} + \frac{b}{5}

Solution steps

\int_{0}^{1} a x^{3} + b x^{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}^{1} a x^{3} d x + \int_{0}^{1} b x^{4} d x

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

\int_{0}^{1} b x^{4} d x = \frac{b}{5}

= \frac{a}{4} + \frac{b}{5}

What is the integral from 0 to 1 of ax^3+bx^4 ?
The integral from 0 to 1 of ax^3+bx^4 is a/4+b/5