What is the integral from 0 to 5 of (x^2-5x) ?

The integral from 0 to 5 of (x^2-5x) is -125/6

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integral from 0 to 5 of (x^2-5x)

\int_{0}^{5} (x^{2} - 5 x) d x

- \frac{125}{6}

Decimal Notation

- 20.83333 \dots

Solution steps

\int_{0}^{5} x^{2} - 5 x 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}^{5} x^{2} d x - \int_{0}^{5} 5 x d x

\int_{0}^{5} x^{2} d x = \frac{125}{3}

\int_{0}^{5} 5 x d x = \frac{125}{2}

= \frac{125}{3} - \frac{125}{2}

Simplify

\frac{125}{3} - \frac{125}{2} : - \frac{125}{6}

= - \frac{125}{6}

n = 0 \sum \infty (- 1)^{n} 2

\frac{21}{x ^{3}}, 1, 1000

x y^{^{'}} - y = 2 x^{2} - x + 1

y^{^{''}} + 16 y = 3 sec (4 t)

f (x) = \frac{8 x + x ^{2}}{( 4 + x ) ^{2}}

What is the integral from 0 to 5 of (x^2-5x) ?
The integral from 0 to 5 of (x^2-5x) is -125/6