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

The integral from 1 to 4 of (x^2+2)/(x^2) is 9/2

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integral from 1 to 4 of (x^2+2)/(x^2)

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

\frac{9}{2}

Decimal Notation

4.5

Solution steps

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

Expand

\frac{x ^{2} + 2}{x ^{2}} : 1 + \frac{2}{x ^{2}}

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

\int_{1}^{4} 1 d x = 3

\int_{1}^{4} \frac{2}{x ^{2}} d x = \frac{3}{2}

= 3 + \frac{3}{2}

Simplify

3 + \frac{3}{2} : \frac{9}{2}

= \frac{9}{2}

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What is the integral from 1 to 4 of (x^2+2)/(x^2) ?
The integral from 1 to 4 of (x^2+2)/(x^2) is 9/2