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

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

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

Compute the boundaries:

\frac{15}{64}

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

Simplify

= - \frac{45}{16}

\frac{\partial}{\partial x} (ln (x + 5 y))

\frac{d}{d x} (x \cdot arcsin (x) + 1 - x^{2})

y = 5 x - x^{2}

\frac{d}{d x} (2 sec (x) + tan (x))

(2 x y - 3 x^{2}) d x + x^{2} d y = 0

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