What is the integral from-1 to 1 of 1-2x^2+x^4 ?

The integral from-1 to 1 of 1-2x^2+x^4 is 16/15

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integral from-1 to 1 of 1-2x^2+x^4

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

\frac{16}{15}

Decimal

1.06666 \dots

Solution steps

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

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

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

\int_{- 1}^{1} x^{4} d x = \frac{2}{5}

= 2 - \frac{4}{3} + \frac{2}{5}

Simplify

2 - \frac{4}{3} + \frac{2}{5} : \frac{16}{15}

= \frac{16}{15}

What is the integral from-1 to 1 of 1-2x^2+x^4 ?
The integral from-1 to 1 of 1-2x^2+x^4 is 16/15