What is the integral from 0 to 3 of (x-2)(2x+1) ?

The integral from 0 to 3 of (x-2)(2x+1) is -3/2

Popular >

integral from 0 to 3 of (x-2)(2x+1)

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

- \frac{3}{2}

Decimal

- 1.5

Solution steps

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

Expand

(x - 2) (2 x + 1) : 2 x^{2} - 3 x - 2

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

\int_{0}^{3} 2 x^{2} d x = 18

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

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

= 18 - \frac{27}{2} - 6

Simplify

18 - \frac{27}{2} - 6 : - \frac{3}{2}

= - \frac{3}{2}

\int_{1}^{3} 3 x^{2} - 10 x + 5 d x

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

\int_{7}^{10} \frac{x}{7} - \frac{7}{x} d x

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

\int_{1}^{2} r^{7} sin (2 r^{4}) d r

What is the integral from 0 to 3 of (x-2)(2x+1) ?
The integral from 0 to 3 of (x-2)(2x+1) is -3/2