What is the integral from 1/2 to 1 of (x^{-3}-12) ?

The integral from 1/2 to 1 of (x^{-3}-12) is -9/2

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integral from 1/2 to 1 of (x^{-3}-12)

\int_{\frac{1}{2}}^{1} (x^{- 3} - 12) d x

- \frac{9}{2}

Decimal

- 4.5

Solution steps

\int_{\frac{1}{2}}^{1} x^{- 3} - 12 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{\frac{1}{2}}^{1} x^{- 3} d x - \int_{\frac{1}{2}}^{1} 12 d x

\int_{\frac{1}{2}}^{1} x^{- 3} d x = \frac{3}{2}

\int_{\frac{1}{2}}^{1} 12 d x = 6

= \frac{3}{2} - 6

Simplify

\frac{3}{2} - 6 : - \frac{9}{2}

= - \frac{9}{2}

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

d er i v a t i v e f (x) = \frac{x ^{2}}{4}

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

x \to 5 lim (\frac{x}{0})

\frac{d}{d x} (cos (x) x^{2})

What is the integral from 1/2 to 1 of (x^{-3}-12) ?
The integral from 1/2 to 1 of (x^{-3}-12) is -9/2