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

The integral from 0 to 2 of (x^2-3x) is -10/3

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integral from 0 to 2 of (x^2-3x)

\int_{0}^{2} (x^{2} - 3 x) d x

- \frac{10}{3}

Decimal

- 3.33333 \dots

Solution steps

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

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

\int_{0}^{2} 3 x d x = 6

= \frac{8}{3} - 6

Simplify

\frac{8}{3} - 6 : - \frac{10}{3}

= - \frac{10}{3}

f (x) = \frac{2 x + 5}{5 x - 1}, at x = - 1

\int \frac{x ^{2} + 6 x}{x ^{3} - x ^{2} + x - 1} d x

x \to 2 lim ((x + 1) \cdot (x + 3))

\frac{\partial}{\partial x} (x e^{- x} (a + b x + c x^{2}))

\frac{\partial}{\partial x} (x^{3} y^{2} - 2 x y^{3})

What is the integral from 0 to 2 of (x^2-3x) ?
The integral from 0 to 2 of (x^2-3x) is -10/3