What is the integral from-3 to 2 of (2x^3-4x) ?

The integral from-3 to 2 of (2x^3-4x) is -45/2

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integral from-3 to 2 of (2x^3-4x)

\int_{- 3}^{2} (2 x^{3} - 4 x) d x

- \frac{45}{2}

Solution steps

\int_{- 3}^{2} 2 x^{3} - 4 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}^{2} 2 x^{3} d x - \int_{- 3}^{2} 4 x d x

\int_{- 3}^{2} 2 x^{3} d x = - \frac{65}{2}

\int_{- 3}^{2} 4 x d x = - 10

= - \frac{65}{2} - (- 10)

Simplify

- \frac{65}{2} - (- 10) : - \frac{45}{2}

= - \frac{45}{2}

\int_{0}^{2} 4 x - x^{2} d x

\int_{1}^{5} t^{2} - 2 t - 8 d t

\int_{- 3}^{2} 12 - x^{2} - x d x

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

\int_{0}^{2} 3 x + 1 d x

What is the integral from-3 to 2 of (2x^3-4x) ?
The integral from-3 to 2 of (2x^3-4x) is -45/2