What is the integral from 1 to 5 of x^2-2x-15 ?

The integral from 1 to 5 of x^2-2x-15 is -128/3

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integral from 1 to 5 of x^2-2x-15

\int_{1}^{5} x^{2} - 2 x - 15 d x

- \frac{128}{3}

Decimal

- 42.66666 \dots

Solution steps

\int_{1}^{5} x^{2} - 2 x - 15 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}^{5} x^{2} d x - \int_{1}^{5} 2 x d x - \int_{1}^{5} 15 d x

\int_{1}^{5} x^{2} d x = \frac{124}{3}

\int_{1}^{5} 2 x d x = 24

\int_{1}^{5} 15 d x = 60

= \frac{124}{3} - 24 - 60

Simplify

\frac{124}{3} - 24 - 60 : - \frac{128}{3}

= - \frac{128}{3}

\int_{1}^{5} (3 x^{2}) d x

\int_{3}^{6} (x - 3)^{2} d x

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

\int_{0}^{4} \frac{3}{5 x + 7} d x

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

What is the integral from 1 to 5 of x^2-2x-15 ?
The integral from 1 to 5 of x^2-2x-15 is -128/3