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

The integral from 0 to 1 of (x^2-2x)(1-x) is -1/4

Popular >

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

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

- \frac{1}{4}

Decimal

- 0.25

Solution steps

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

Expand

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

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

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

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

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

= - \frac{1}{4} + 1 - 1

Simplify

= - \frac{1}{4}

\int_{x}^{0} e^{- 15 t} d t

\int_{0}^{1} 7 x + x d x

\int_{x^{2}}^{π} sin (θ^{3}) d θ

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

\int_{1}^{c o s (x)} 8 x^{7} d x

What is the integral from 0 to 1 of (x^2-2x)(1-x) ?
The integral from 0 to 1 of (x^2-2x)(1-x) is -1/4