What is the integral from 1 to 10 of x 2/81 (x-1) ?

The integral from 1 to 10 of x 2/81 (x-1) is 7

Popular >

integral from 1 to 10 of x 2/81 (x-1)

\int_{1}^{10} x \frac{2}{81} (x - 1) d x

7

Solution steps

\int_{1}^{10} x \frac{2}{81} (x - 1) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{81} \cdot \int_{1}^{10} x (x - 1) d x

Expand

x (x - 1) : x^{2} - x

= \frac{2}{81} \cdot \int_{1}^{10} x^{2} - x 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

= \frac{2}{81} (\int_{1}^{10} x^{2} d x - \int_{1}^{10} x d x)

\int_{1}^{10} x^{2} d x = 333

\int_{1}^{10} x d x = \frac{99}{2}

= \frac{2}{81} (333 - \frac{99}{2})

Simplify

\frac{2}{81} (333 - \frac{99}{2}) : 7

= 7

\int_{3}^{\infty} e^{- s t} d t

\int_{0}^{9} (81 - x^{2}) d x

\int_{0}^{5} e^{x^{2}} d x

\int_{- 4}^{3} - x^{2} - 3 x d x

\int_{0}^{1} x 63 x^{2} + 1 d x

What is the integral from 1 to 10 of x 2/81 (x-1) ?
The integral from 1 to 10 of x 2/81 (x-1) is 7