What is the integral from 1 to 2 of (2x^3-x^4) ?

The integral from 1 to 2 of (2x^3-x^4) is 13/10

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integral from 1 to 2 of (2x^3-x^4)

\int_{1}^{2} (2 x^{3} - x^{4}) d x

\frac{13}{10}

Decimal

1.3

Solution steps

\int_{1}^{2} 2 x^{3} - 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_{1}^{2} 2 x^{3} d x - \int_{1}^{2} x^{4} d x

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

\int_{1}^{2} x^{4} d x = \frac{31}{5}

= \frac{15}{2} - \frac{31}{5}

Simplify

\frac{15}{2} - \frac{31}{5} : \frac{13}{10}

= \frac{13}{10}

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What is the integral from 1 to 2 of (2x^3-x^4) ?
The integral from 1 to 2 of (2x^3-x^4) is 13/10