What is the integral from 0 to 3 of-2x^3 ?

The integral from 0 to 3 of-2x^3 is -81/2

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integral from 0 to 3 of-2x^3

\int_{0}^{3} - 2 x^{3} d x

- \frac{81}{2}

Decimal Notation

- 40.5

Solution steps

\int_{0}^{3} - 2 x^{3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int_{0}^{3} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{0}^{3}

= - 2 [\frac{x ^{4}}{4}]_{0}^{3}

Compute the boundaries:

\frac{81}{4}

= - 2 \cdot \frac{81}{4}

Simplify

= - \frac{81}{2}

\int_{0}^{2} (x - 3 y^{2}) d x

\int_{- 2}^{1} x^{2} - 6 x + 12 d x

\int_{1}^{a} \frac{ln ( x )}{x} d x

\int_{0}^{1} ln (1 + 2 x) d x

\int_{0}^{1} \frac{44}{x ^{2} - 121} d x

What is the integral from 0 to 3 of-2x^3 ?
The integral from 0 to 3 of-2x^3 is -81/2