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

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

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integral from 0 to 1 of (x^2-4x+2)

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

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

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

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

\int_{0}^{1} 4 x d x = 2

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

= \frac{1}{3} - 2 + 2

Simplify

= \frac{1}{3}

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