What is the integral from 1/2 to 1 of (x^{-3}-25) ?

The integral from 1/2 to 1 of (x^{-3}-25) is -11

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integral from 1/2 to 1 of (x^{-3}-25)

\int_{\frac{1}{2}}^{1} (x^{- 3} - 25) d x

- 11

Solution steps

\int_{\frac{1}{2}}^{1} x^{- 3} - 25 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} 25 d x

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

\int_{\frac{1}{2}}^{1} 25 d x = \frac{25}{2}

= \frac{3}{2} - \frac{25}{2}

Simplify

\frac{3}{2} - \frac{25}{2} : - 11

= - 11

y^{^{''}} + \frac{1}{x} y^{^{'}} = 0

y^{^{''}} + 2 x = 6 x^{2}, y (0) = 3

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What is the integral from 1/2 to 1 of (x^{-3}-25) ?
The integral from 1/2 to 1 of (x^{-3}-25) is -11