What is the integral from 0 to 1 of (6x^2+15/2 x^3) ?

The integral from 0 to 1 of (6x^2+15/2 x^3) is 31/8

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integral from 0 to 1 of (6x^2+15/2 x^3)

\int_{0}^{1} (6 x^{2} + \frac{15}{2} x^{3}) d x

\frac{31}{8}

Decimal Notation

3.875

Solution steps

\int_{0}^{1} 6 x^{2} + \frac{15}{2} 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} 6 x^{2} d x + \int_{0}^{1} \frac{15}{2} x^{3} d x

\int_{0}^{1} 6 x^{2} d x = 2

\int_{0}^{1} \frac{15}{2} x^{3} d x = \frac{15}{8}

= 2 + \frac{15}{8}

Simplify

2 + \frac{15}{8} : \frac{31}{8}

= \frac{31}{8}

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What is the integral from 0 to 1 of (6x^2+15/2 x^3) ?
The integral from 0 to 1 of (6x^2+15/2 x^3) is 31/8