What is the integral from 1 to 2 of (8-2x)/(x^3) ?

The integral from 1 to 2 of (8-2x)/(x^3) is 2

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integral from 1 to 2 of (8-2x)/(x^3)

\int_{1}^{2} \frac{8 - 2 x}{x ^{3}} d x

2

Solution steps

\int_{1}^{2} \frac{8 - 2 x}{x ^{3}} d x

Expand

\frac{8 - 2 x}{x ^{3}} : \frac{8}{x ^{3}} - \frac{2}{x ^{2}}

= \int_{1}^{2} \frac{8}{x ^{3}} - \frac{2}{x ^{2}} 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_{1}^{2} \frac{8}{x ^{3}} d x - \int_{1}^{2} \frac{2}{x ^{2}} d x

\int_{1}^{2} \frac{8}{x ^{3}} d x = 3

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

= 3 - 1

Simplify

= 2

\int_{0}^{4} 32 - 2 x^{2} d x

\int_{17}^{x} \frac{1}{t} d t

\int_{x}^{1} sin^{2} (t) d t

\int_{- 1}^{1} t^{3} d t

\int_{0}^{2} t 1 + 4 t^{2} d t

What is the integral from 1 to 2 of (8-2x)/(x^3) ?
The integral from 1 to 2 of (8-2x)/(x^3) is 2