What is the integral from 1 to 1000 of (33)/(x^3) ?

The integral from 1 to 1000 of (33)/(x^3) is 32999967/2000000

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integral from 1 to 1000 of (33)/(x^3)

\int_{1}^{1000} \frac{33}{x ^{3}} d x

\frac{32999967}{2000000}

Decimal Notation

16.4999835

Solution steps

\int_{1}^{1000} \frac{33}{x ^{3}} d x

Take the constant out:

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

= 33 \cdot \int_{1}^{1000} \frac{1}{x ^{3}} d x

Apply the Power Rule

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

= 33 [- \frac{1}{2 x ^{2}}]_{1}^{1000}

Compute the boundaries:

\frac{999999}{2000000}

= 33 \cdot \frac{999999}{2000000}

Simplify

= \frac{32999967}{2000000}

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What is the integral from 1 to 1000 of (33)/(x^3) ?
The integral from 1 to 1000 of (33)/(x^3) is 32999967/2000000