What is the integral from-1 to 4 of x^2-4x-5 ?

The integral from-1 to 4 of x^2-4x-5 is -100/3

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integral from-1 to 4 of x^2-4x-5

\int_{- 1}^{4} x^{2} - 4 x - 5 d x

- \frac{100}{3}

Decimal

- 33.33333 \dots

Solution steps

\int_{- 1}^{4} x^{2} - 4 x - 5 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}^{4} x^{2} d x - \int_{- 1}^{4} 4 x d x - \int_{- 1}^{4} 5 d x

\int_{- 1}^{4} x^{2} d x = \frac{65}{3}

\int_{- 1}^{4} 4 x d x = 30

\int_{- 1}^{4} 5 d x = 25

= \frac{65}{3} - 30 - 25

Simplify

\frac{65}{3} - 30 - 25 : - \frac{100}{3}

= - \frac{100}{3}

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What is the integral from-1 to 4 of x^2-4x-5 ?
The integral from-1 to 4 of x^2-4x-5 is -100/3