# Find the area S of the region

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width.

Then find the area S of the region.

1. How do i know whether to integrate with respect to x or y?

2. is 2/x the same thing as x^-2 ?? (if not how do i rewrite it) ?

help.

i graphed it and didn't know what to do with the x = 7.

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## Answers and Replies

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Office_Shredder
Staff Emeritus
Gold Member
x=7 is going to be a vertical line, all points of the form (7,y).

You can integrate with respect to either x or y, try writing both integrals out and see which one looks easier

$$\frac{2}{x} =/= x^{-2}$$ I don't know why you would think that... $$\frac{2}{x} = 2* \frac{1}{x}$$ If you're unsure of how fractions and exponentials work this is going to be a difficult problem to solve

HallsofIvy
Homework Helper
I would start by determining where the two graphs intersect. Where is
$$y= \frac{2}{x}= \frac{2}{x^2}$$?

Now, if y is a number between those two y values, for what x values is y= 1/x or y= 1/x2?
If x is number between the two x-values of the intersection points, what are y= 1/x and y= 1/x2?

Which of those is easier to integrate?

i set the = and i think i got (0,1) is that right?

and im not following the second part, sorry.

HallsofIvy