What is the integral from 2 to 4 of (x^2-4)/(x^2) ?

The integral from 2 to 4 of (x^2-4)/(x^2) is 1

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integral from 2 to 4 of (x^2-4)/(x^2)

\int_{2}^{4} \frac{x ^{2} - 4}{x ^{2}} d x

1

Solution steps

\int_{2}^{4} \frac{x ^{2} - 4}{x ^{2}} d x

Expand

\frac{x ^{2} - 4}{x ^{2}} : 1 - \frac{4}{x ^{2}}

= \int_{2}^{4} 1 - \frac{4}{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_{2}^{4} 1 d x - \int_{2}^{4} \frac{4}{x ^{2}} d x

\int_{2}^{4} 1 d x = 2

\int_{2}^{4} \frac{4}{x ^{2}} d x = 1

= 2 - 1

Simplify

= 1

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What is the integral from 2 to 4 of (x^2-4)/(x^2) ?
The integral from 2 to 4 of (x^2-4)/(x^2) is 1