What is the integral from 6 to 100 of 2x^{-3} ?

The integral from 6 to 100 of 2x^{-3} is 2491/90000

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integral from 6 to 100 of 2x^{-3}

\int_{6}^{100} 2 x^{- 3} d x

\frac{2491}{90000}

Decimal Notation

0.02767 \dots

Solution steps

\int_{6}^{100} 2 x^{- 3} d x

Take the constant out:

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

= 2 \cdot \int_{6}^{100} x^{- 3} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{6}^{100}

= 2 [- \frac{1}{2 x ^{2}}]_{6}^{100}

Compute the boundaries:

\frac{2491}{180000}

= 2 \cdot \frac{2491}{180000}

Simplify

= \frac{2491}{90000}

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What is the integral from 6 to 100 of 2x^{-3} ?
The integral from 6 to 100 of 2x^{-3} is 2491/90000