Computing Areas Between Curves
Have you ever heard the famous comedy routine by Abbott and Costello called, “Who’s on First?”
Well, if you’re anything like me sometimes, you can be left feeling a little like Costello, who is hopelessly confused as to the players on a baseball team who have names like “who,” “what” and “I don’t know.”
Thankfully, finding the area between curves doesn’t have to be confusing… I’ve got tricks!
What tricks?
Identifying which function is on top and which is on the bottom?
But let me back up a bit. As we already know, an area is a measure of how much space there is inside a region or object.
Formula for Calculating the Area Between Two Curves
And we know from experience that when finding the area of known geometric shapes such as rectangles or triangles, it’s helpful to have a formula.
Well, there’s a very simple formula for finding the area between two curves.
Now for the first part of the trick: what do the pieces of the formula mean?
And the second part of the trick is knowing our orientation.
After graphing each function, which determines the enclosed region, we identify the top and bottom, or as Paul’s Online Notes says, the “larger” function minus the “smaller” function, by deciding which axis to “stand on.”
How do we decide the right axis?
Well, we must determine if we have a distinct “top” function and a distinct “bottom” function perpendicular to either the x or y-axis.
Determining Area by Horizontal or Vertical Strips
After that, we plug into our formula and integrate using our Integration rules.
Don’t worry; it’s really easy!
Together will remind ourselves how to graph all different types of functions and learn how to find points of intersection, which is necessary for determining the interval for which we will integrate over (i.e., finding the limits of integration).
And lastly, we will briefly talk about how area helps us to find volume.
Area Between Two Curves Video
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