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

The integral from 0 to-3 of-x^2-3x is -9/2

Popular >

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

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

- \frac{9}{2}

Decimal Notation

- 4.5

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

\int_{- 3}^{0} x^{2} d x = 9

\int_{- 3}^{0} 3 x d x = - \frac{27}{2}

= - (- 9 - (- \frac{27}{2}))

Simplify

- (- 9 - (- \frac{27}{2})) : - \frac{9}{2}

= - \frac{9}{2}

\int_{- 1}^{4} (4 x - 3) (x - 3) d x

\int_{0}^{5} (25 - x^{2})^{\frac{1}{2}} d x

\int_{- 1}^{0} (2 + 1 - x^{2}) d x

\int_{0}^{4} (2 + x) d x

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

What is the integral from 0 to-3 of-x^2-3x ?
The integral from 0 to-3 of-x^2-3x is -9/2