What is the integral from-2 to 3 of 2x^3-8x^2+2x+12 ?

The integral from-2 to 3 of 2x^3-8x^2+2x+12 is 25/6

Popular >

integral from-2 to 3 of 2x^3-8x^2+2x+12

\int_{- 2}^{3} 2 x^{3} - 8 x^{2} + 2 x + 12 d x

\frac{25}{6}

Decimal Notation

4.16666 \dots

Solution steps

\int_{- 2}^{3} 2 x^{3} - 8 x^{2} + 2 x + 12 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_{- 2}^{3} 2 x^{3} d x - \int_{- 2}^{3} 8 x^{2} d x + \int_{- 2}^{3} 2 x d x + \int_{- 2}^{3} 12 d x

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

\int_{- 2}^{3} 8 x^{2} d x = \frac{280}{3}

\int_{- 2}^{3} 2 x d x = 5

\int_{- 2}^{3} 12 d x = 60

= \frac{65}{2} - \frac{280}{3} + 5 + 60

Simplify

\frac{65}{2} - \frac{280}{3} + 5 + 60 : \frac{25}{6}

= \frac{25}{6}

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

\int_{1}^{6} x^{5} ln (x) d x

\int_{0}^{y} \frac{x}{x ^{2} + y ^{2}} d y

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

\int_{1}^{2} (\frac{2}{3} + 2 z) d z

What is the integral from-2 to 3 of 2x^3-8x^2+2x+12 ?
The integral from-2 to 3 of 2x^3-8x^2+2x+12 is 25/6