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

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

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integral from-1 to 1 of-x^2+2-x^2

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

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

\int_{- 1}^{1} - x^{2} + 2 - x^{2} 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_{0}^{1} \frac{x ^{3}}{2 ( 1 + x ^{4} )} d x

\int_{- 4}^{4} x^{3} - 16 x d x

\int_{1}^{2} x^{3} - x^{2} d x

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

\int_{1}^{\infty} x \cdot \frac{4}{x ^{5}} d x

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