AREA BETWEEN CURVES

Question

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to 𝑥x or 𝑦y. Then find the area of the region.

y=1/x

y=1/x^2

x=3

Answer 1

I'm assuming that we are talking about the area from the point of intersection (1,1) and the vertical, x = 3. In that case we want to find the integral of (1/x - 1/x²) dx from 1 to 3. If you graph the curves, you can see that 1/x will be above 1/x² in this region and that the vertical height of the differential rectangles, ydx, will have y equal to the difference in the functions.

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