What is the integral from 0 to 8/9 of 8x-9x^2 ?

The integral from 0 to 8/9 of 8x-9x^2 is 256/243

Popular >

integral from 0 to 8/9 of 8x-9x^2

\int_{0}^{\frac{8}{9}} 8 x - 9 x^{2} d x

\frac{256}{243}

Decimal

1.05349 \dots

Solution steps

\int_{0}^{\frac{8}{9}} 8 x - 9 x^{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_{0}^{\frac{8}{9}} 8 x d x - \int_{0}^{\frac{8}{9}} 9 x^{2} d x

\int_{0}^{\frac{8}{9}} 8 x d x = \frac{256}{81}

\int_{0}^{\frac{8}{9}} 9 x^{2} d x = \frac{512}{243}

= \frac{256}{81} - \frac{512}{243}

Simplify

\frac{256}{81} - \frac{512}{243} : \frac{256}{243}

= \frac{256}{243}

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

\int_{0}^{5} \frac{1}{9 - 2 x} d x

\int_{0}^{3} x^{2} - x - 6 d x

\int_{- 1}^{1} (4 - 9 x) d x

\int_{0}^{π} x cos (a x) d x

What is the integral from 0 to 8/9 of 8x-9x^2 ?
The integral from 0 to 8/9 of 8x-9x^2 is 256/243