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

The integral from 1 to 2 of x(x-1)(x-2) is -1/4

Popular >

integral from 1 to 2 of x(x-1)(x-2)

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

- \frac{1}{4}

Decimal

- 0.25

Solution steps

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

Expand

x (x - 1) (x - 2) : x^{3} - 3 x^{2} + 2 x

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

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

\int_{1}^{2} 3 x^{2} d x = 7

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

= \frac{15}{4} - 7 + 3

Simplify

\frac{15}{4} - 7 + 3 : - \frac{1}{4}

= - \frac{1}{4}

\int_{0}^{20} - 0.4 x^{2} + 1000 - 840 d x

\int_{- 1}^{2} (t i + 3 t^{2} j + 4 t^{3} k) d t

\int_{1}^{4} x e^{x^{2}} d x

\int_{- 7}^{4} x^{2} d x

\int_{0}^{1} x + 1 d x

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