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

The integral from-1 to 1 of (1-x^2)-(x^2-1) is 8/3

Popular >

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

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

\frac{8}{3}

Solution steps

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

Simplify

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

\int_{- 1}^{1} 2 x^{2} d x = \frac{4}{3}

\int_{- 1}^{1} 2 d x = 4

= - \frac{4}{3} + 4

Simplify

- \frac{4}{3} + 4 : \frac{8}{3}

= \frac{8}{3}

\int_{\frac{π}{4}}^{\frac{π}{2}} x csc^{2} (x) d x

\int_{0}^{\frac{π}{4}} tan^{2} (t) d t

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

\int_{- 2}^{1} 2 d x

\int_{- π}^{π} sin (n x) sin (2 x) d x

What is the integral from-1 to 1 of (1-x^2)-(x^2-1) ?
The integral from-1 to 1 of (1-x^2)-(x^2-1) is 8/3