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

The integral from-2 to 2 of 2x^2-(x^4-2x^2) is 128/15

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

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

\frac{128}{15}

Decimal

8.53333 \dots

Solution steps

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

Simplify

= \int_{- 2}^{2} - x^{4} + 4 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_{- 2}^{2} x^{4} d x + \int_{- 2}^{2} 4 x^{2} d x

\int_{- 2}^{2} x^{4} d x = \frac{64}{5}

\int_{- 2}^{2} 4 x^{2} d x = \frac{64}{3}

= - \frac{64}{5} + \frac{64}{3}

Simplify

- \frac{64}{5} + \frac{64}{3} : \frac{128}{15}

= \frac{128}{15}

\int_{0}^{x} 3 y d y

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

\int_{- \frac{π}{4}}^{\frac{π}{4}} cos (θ) d θ

\int_{0}^{1.6} g (x) d x

\int_{0}^{3} 2 x - 5 d x

What is the integral from-2 to 2 of 2x^2-(x^4-2x^2) ?
The integral from-2 to 2 of 2x^2-(x^4-2x^2) is 128/15