What is the integral from 0 to 1 of 9x^8(2-x^9) ?

The integral from 0 to 1 of 9x^8(2-x^9) is 3/2

Popular >

integral from 0 to 1 of 9x^8(2-x^9)

\int_{0}^{1} 9 x^{8} (2 - x^{9}) d x

\frac{3}{2}

Decimal

1.5

Solution steps

\int_{0}^{1} 9 x^{8} (2 - x^{9}) d x

Take the constant out:

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

= 9 \cdot \int_{0}^{1} x^{8} (2 - x^{9}) d x

Expand

x^{8} (2 - x^{9}) : 2 x^{8} - x^{17}

= 9 \cdot \int_{0}^{1} 2 x^{8} - x^{17} 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

= 9 (\int_{0}^{1} 2 x^{8} d x - \int_{0}^{1} x^{17} d x)

\int_{0}^{1} 2 x^{8} d x = \frac{2}{9}

\int_{0}^{1} x^{17} d x = \frac{1}{18}

= 9 (\frac{2}{9} - \frac{1}{18})

Simplify

9 (\frac{2}{9} - \frac{1}{18}) : \frac{3}{2}

= \frac{3}{2}

\int_{2}^{3} x^{4} + 4 x - 6 d x

\int_{0}^{a} \frac{b}{a ^{2}} (x - a)^{2} d x

\int_{4}^{- 4} 1

\int_{0}^{2 π} 2 x cos (x) d x

\int_{2}^{4} x - 9 d x

What is the integral from 0 to 1 of 9x^8(2-x^9) ?
The integral from 0 to 1 of 9x^8(2-x^9) is 3/2