What is the integral from-1 to 1 of (x^5-x^6) ?

The integral from-1 to 1 of (x^5-x^6) is -2/7

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integral from-1 to 1 of (x^5-x^6)

\int_{- 1}^{1} (x^{5} - x^{6}) d x

- \frac{2}{7}

Decimal

- 0.28571 \dots

Solution steps

\int_{- 1}^{1} x^{5} - x^{6} 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} x^{5} d x - \int_{- 1}^{1} x^{6} d x

\int_{- 1}^{1} x^{5} d x = 0

\int_{- 1}^{1} x^{6} d x = \frac{2}{7}

= 0 - \frac{2}{7}

Simplify

= - \frac{2}{7}

What is the integral from-1 to 1 of (x^5-x^6) ?
The integral from-1 to 1 of (x^5-x^6) is -2/7