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

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

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

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

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

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

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

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

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

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

Simplify

= \frac{1}{3}

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