What is the integral from 0 to 1 of-x^6+4x^4-2x^2+1 ?

The integral from 0 to 1 of-x^6+4x^4-2x^2+1 is 104/105

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 1 of-x^6+4x^4-2x^2+1

\int_{0}^{1} - x^{6} + 4 x^{4} - 2 x^{2} + 1 d x

\frac{104}{105}

Decimal

0.99047 \dots

Solution steps

\int_{0}^{1} - x^{6} + 4 x^{4} - 2 x^{2} + 1 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_{0}^{1} x^{6} d x + \int_{0}^{1} 4 x^{4} d x - \int_{0}^{1} 2 x^{2} d x + \int_{0}^{1} 1 d x

\int_{0}^{1} x^{6} d x = \frac{1}{7}

\int_{0}^{1} 4 x^{4} d x = \frac{4}{5}

\int_{0}^{1} 2 x^{2} d x = \frac{2}{3}

\int_{0}^{1} 1 d x = 1

= - \frac{1}{7} + \frac{4}{5} - \frac{2}{3} + 1

Simplify

- \frac{1}{7} + \frac{4}{5} - \frac{2}{3} + 1 : \frac{104}{105}

= \frac{104}{105}

What is the integral from 0 to 1 of-x^6+4x^4-2x^2+1 ?
The integral from 0 to 1 of-x^6+4x^4-2x^2+1 is 104/105