What is the integral from-1 to 0 of (x^3-x^2-2x) ?

The integral from-1 to 0 of (x^3-x^2-2x) is 5/12

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integral from-1 to 0 of (x^3-x^2-2x)

\int_{- 1}^{0} (x^{3} - x^{2} - 2 x) d x

\frac{5}{12}

Decimal Notation

0.41666 \dots

Solution steps

\int_{- 1}^{0} x^{3} - x^{2} - 2 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_{- 1}^{0} x^{3} d x - \int_{- 1}^{0} x^{2} d x - \int_{- 1}^{0} 2 x d x

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

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

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

= - \frac{1}{4} - \frac{1}{3} - (- 1)

Simplify

- \frac{1}{4} - \frac{1}{3} - (- 1) : \frac{5}{12}

= \frac{5}{12}

f (x) = - 3 sin (3 x)

\int \frac{1}{7 x ^{2} - 8} d x

x \to - 3 lim (- x^{2} + 8 x - 9)

\int \frac{1}{x ^{2}} sin (\frac{π}{x}) d x

What is the integral from-1 to 0 of (x^3-x^2-2x) ?
The integral from-1 to 0 of (x^3-x^2-2x) is 5/12