What is the integral from 2 to 1 of (12x^{-5}) ?

The integral from 2 to 1 of (12x^{-5}) is -45/16

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integral from 2 to 1 of (12x^{-5})

\int_{2}^{1} (12 x^{- 5}) d x

- \frac{45}{16}

Decimal

- 2.8125

Solution steps

\int_{2}^{1} 12 x^{- 5} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{2} 12 x^{- 5} d x

Take the constant out:

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

= - 12 \cdot \int_{1}^{2} x^{- 5} d x

Apply the Power Rule

= - 12 [- \frac{1}{4 x ^{4}}]_{1}^{2}

Compute the boundaries:

\frac{15}{64}

= - 12 \cdot \frac{15}{64}

Simplify

= - \frac{45}{16}

What is the integral from 2 to 1 of (12x^{-5}) ?
The integral from 2 to 1 of (12x^{-5}) is -45/16