What is the integral from-2 to 5 of |-x^3+9x| ?

The integral from-2 to 5 of |-x^3+9x| is 393/4

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integral from-2 to 5 of |-x^3+9x|

\int_{- 2}^{5} - x^{3} + 9 x d x

\frac{393}{4}

Decimal Notation

98.25

Solution steps

\int_{- 2}^{5} - x^{3} + 9 x d x

Eliminate Absolutes

= \int_{- 2}^{0} x^{3} - 9 x d x + \int_{0}^{3} - x^{3} + 9 x d x + \int_{3}^{5} x^{3} - 9 x d x

\int_{- 2}^{0} x^{3} - 9 x d x = 14

\int_{0}^{3} - x^{3} + 9 x d x = \frac{81}{4}

\int_{3}^{5} x^{3} - 9 x d x = 64

= 14 + \frac{81}{4} + 64

Simplify

14 + \frac{81}{4} + 64 : \frac{393}{4}

= \frac{393}{4}

\frac{d}{d x} (4 cot (x))

f (x) = - 5 e^{- 2.5 x^{2}} x

x \to 0 lim (x^{3} + 2^{2} - x)

x y \frac{d y}{d x} = 1 + y^{2}

y^{^{'}} - \frac{2}{x} y = \frac{y ^{5}}{x ^{2}}

What is the integral from-2 to 5 of |-x^3+9x| ?
The integral from-2 to 5 of |-x^3+9x| is 393/4