What is the integral from 1 to 1000 of 9/(x^3) ?

The integral from 1 to 1000 of 9/(x^3) is 8999991/2000000

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integral from 1 to 1000 of 9/(x^3)

\int_{1}^{1000} \frac{9}{x ^{3}} d x

\frac{8999991}{2000000}

Decimal Notation

4.4999955

Solution steps

\int_{1}^{1000} \frac{9}{x ^{3}} d x

Take the constant out:

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

= 9 \cdot \int_{1}^{1000} \frac{1}{x ^{3}} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{1}^{1000}

= 9 [- \frac{1}{2 x ^{2}}]_{1}^{1000}

Compute the boundaries:

\frac{999999}{2000000}

= 9 \cdot \frac{999999}{2000000}

Simplify

= \frac{8999991}{2000000}

t^{2} + e^{- 2 t} sin (3 t)

x \to - 1 lim (3 x^{3} + 2 x^{2} + 3)

x \to 0 + lim (e^{(\frac{1}{x})})

\frac{y ^{2} - 2}{2 y ^{2}}

\int \frac{x ^{3} - 2 x ^{2} + 1}{x - 3} d x

What is the integral from 1 to 1000 of 9/(x^3) ?
The integral from 1 to 1000 of 9/(x^3) is 8999991/2000000