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

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

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

\int_{- 1}^{0} (x^{2} - 2 x - \frac{1}{3}) d x

1

Solution steps

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

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

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

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

= \frac{1}{3} - (- 1) - \frac{1}{3}

Simplify

= 1

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