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

The integral from-1 to 2 of x^3-x^2-2x is -9/4

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integral from-1 to 2 of x^3-x^2-2x

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

- \frac{9}{4}

Decimal

- 2.25

Solution steps

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

\int_{- 1}^{2} x^{3} d x = \frac{15}{4}

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

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

= \frac{15}{4} - 3 - 3

Simplify

\frac{15}{4} - 3 - 3 : - \frac{9}{4}

= - \frac{9}{4}

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

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

\int_{0}^{4} (x - 1)^{2} d x

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

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

What is the integral from-1 to 2 of x^3-x^2-2x ?
The integral from-1 to 2 of x^3-x^2-2x is -9/4