What is the integral from 0 to 4 of x^2-2x-3 ?

The integral from 0 to 4 of x^2-2x-3 is -20/3

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integral from 0 to 4 of x^2-2x-3

\int_{0}^{4} x^{2} - 2 x - 3 d x

- \frac{20}{3}

Decimal

- 6.66666 \dots

Solution steps

\int_{0}^{4} x^{2} - 2 x - 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_{0}^{4} x^{2} d x - \int_{0}^{4} 2 x d x - \int_{0}^{4} 3 d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 2 x d x = 16

\int_{0}^{4} 3 d x = 12

= \frac{64}{3} - 16 - 12

Simplify

\frac{64}{3} - 16 - 12 : - \frac{20}{3}

= - \frac{20}{3}

What is the integral from 0 to 4 of x^2-2x-3 ?
The integral from 0 to 4 of x^2-2x-3 is -20/3