What is the integral from 0 to 3 of x^3-x^2-6x ?

The integral from 0 to 3 of x^3-x^2-6x is -63/4

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integral from 0 to 3 of x^3-x^2-6x

\int_{0}^{3} x^{3} - x^{2} - 6 x d x

- \frac{63}{4}

Decimal

- 15.75

Solution steps

\int_{0}^{3} x^{3} - x^{2} - 6 x 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}^{3} x^{3} d x - \int_{0}^{3} x^{2} d x - \int_{0}^{3} 6 x d x

\int_{0}^{3} x^{3} d x = \frac{81}{4}

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 6 x d x = 27

= \frac{81}{4} - 9 - 27

Simplify

\frac{81}{4} - 9 - 27 : - \frac{63}{4}

= - \frac{63}{4}

\frac{\partial}{\partial x} ((x + 20) y)

\int (x + 5)^{4} d x

\frac{d}{d x} (ln (2 sin (x)))

y = (3 - e^{x})^{3}

\frac{d y}{d x} = \frac{8 x}{4 y}

What is the integral from 0 to 3 of x^3-x^2-6x ?
The integral from 0 to 3 of x^3-x^2-6x is -63/4