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

The integral from 0 to 2 of (x^2-5x) is -22/3

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

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

- \frac{22}{3}

Decimal Notation

- 7.33333 \dots

Solution steps

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 5 x d x = 10

= \frac{8}{3} - 10

Simplify

\frac{8}{3} - 10 : - \frac{22}{3}

= - \frac{22}{3}

y^{^{'}} + y = 5 cos (2 t)

\frac{( 3 s + 7 )}{s ^{2} + 4 s + 3}

\frac{d}{d x} (x^{4} \cdot sin (x) \cdot sin (3 x))

\frac{\partial}{\partial t} (s^{2} + t^{2})

What is the integral from 0 to 2 of (x^2-5x) ?
The integral from 0 to 2 of (x^2-5x) is -22/3