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

The integral from-1 to 3 of x(2x+3-x^2) is 32/3

Popular >

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

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

\frac{32}{3}

Decimal Notation

10.66666 \dots

Solution steps

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

Expand

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

= \int_{- 1}^{3} 2 x^{2} + 3 x - x^{3} 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_{- 1}^{3} 2 x^{2} d x + \int_{- 1}^{3} 3 x d x - \int_{- 1}^{3} x^{3} d x

\int_{- 1}^{3} 2 x^{2} d x = \frac{56}{3}

\int_{- 1}^{3} 3 x d x = 12

\int_{- 1}^{3} x^{3} d x = 20

= \frac{56}{3} + 12 - 20

Simplify

\frac{56}{3} + 12 - 20 : \frac{32}{3}

= \frac{32}{3}

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

\int_{0}^{1} \frac{1 + 6 t}{1 + 2 t} d t

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

\int_{0}^{1} \frac{4}{3} t^{\frac{3}{2}} (t + 2) d t

\int_{0}^{\infty} x (e^{- x}) d x

What is the integral from-1 to 3 of x(2x+3-x^2) ?
The integral from-1 to 3 of x(2x+3-x^2) is 32/3