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

The integral from 0 to 1 of x^3-3x^2+2x is 1/4

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integral from 0 to 1 of x^3-3x^2+2x

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

\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}

y = x^{2} - 5 x + 5

\int x^{2} (6 - x) d x

2 y^{^{''}} - y^{^{'}} - y = 6 e^{- \frac{x}{2}}

\frac{d}{d x} (\frac{7}{x + 5})

\frac{d}{d x} (sin (4 x + 3))

What is the integral from 0 to 1 of x^3-3x^2+2x ?
The integral from 0 to 1 of x^3-3x^2+2x is 1/4