# Find the area of region between curves

• Apr 9th 2013, 08:43 AM
Steelers72
Find the area of region between curves
Sketch the region enclosed by the given curves.y = 2/x, y = 8x, y =1/8x x > 0

 http://www.webassign.net/waplots/8/d...c6e275f0f4.gif

Find its area.

I found that this is the correct graph
In order to find its area, do we need to take the integral of each side and add them together? How do we find the limits? Do we need to find in terms of x instead of the y= values they give us?

I thought for graph problems you subtract the two equations but I'm not sure..
• Apr 9th 2013, 09:21 AM
topsquark
Re: Find the area of region between curves
Quote:

Originally Posted by Steelers72
Sketch the region enclosed by the given curves.y = 2/x, y = 8x, y =1/8x x > 0

 http://www.webassign.net/waplots/8/d...c6e275f0f4.gif

Find its area.

I found that this is the correct graph
In order to find its area, do we need to take the integral of each side and add them together? How do we find the limits? Do we need to find in terms of x instead of the y= values they give us?

I thought for graph problems you subtract the two equations but I'm not sure..

Start by finding the two intersection points. Then I'd integrate over x in the two regions.

-Dan
• Apr 9th 2013, 09:59 AM
Re: Find the area of region between curves
You do subtract then integrate; but as topsquark pointed out, you need to find the intersection point of the "curves" (i.e. functions) bounding the region on the top. (See your vertical blue line.) Then you can split the region up into two areas, bounded above and below by only two functions, (one area to the left of that blue line, and one to the right.)
• Apr 9th 2013, 10:34 AM
HallsofIvy
Re: Find the area of region between curves
More important than "thinking" that "for graph problem you subtract", you should understand why you subtract. Think back to "Riemann sums"- you want to break the area into many thin rectangles. The area of each rectangle is the "thickness", dx, times the length- that is the difference between the two formulas.
• Apr 9th 2013, 04:41 PM
Steelers72
Re: Find the area of region between curves
Thanks guys.

Would the limits be .5 and 4? I followed the blue lines down and x= .5 and x=4

so integral 0 to .5 [1/8x] - integral .5 to 4 [2/x] ? Am I on the right track?

If so,
http://www4a.wolframalpha.com/Calcul...27&w=99.&h=37.
• Apr 9th 2013, 07:09 PM
Re: Find the area of region between curves
Yes, but you should make sure x = .5 is the intersection point... with algebra...!
• Apr 9th 2013, 07:48 PM
ibdutt
Re: Find the area of region between curves
Let us first name the equations:
y = 8x ---- 1.
y = 2/x ---2.
y = (1/8) x
I would suggest that first you find the x coordinates of points of intersection.
Intersection of 1 and 2 x = 1/2
Intersection of 2 and 3 x = 4
Now the required area = (area under the curve 1 from x = 0 to x = 1/2) + (area under the curve 2 from x = 01/2 to x = 4) - (area under the curve 3 from x = 0 to x = 4)
Now use integration to get the result