How Do You Calculate the Area Between Two Curves?

[Jay J]

Homework Statement

Decide whether to integrate with respect to x or y.
Then find the area bounded by these graphs
x = 2y^2 and x+y = 1

Homework Equations

equations for integration and anti derivatives.

The Attempt at a Solution

i put them in terms of x and have x = 2y^2 and x = y-1.

then do i just graph it and take an integral ?

Any help would be appreciated

Thanks

Jay J

 

[Mark44]

You shouldn't ask if you should graph the two curves -- you should already have done that! From the graph you can see that the curves intersect at two points, and these will determine your limits of integration.

Also, if you integrate with respect to x (and subtract the y values of the two curves), you will need to have two different integrals. If you integrate with respect to y (and subtract the x values on the curves), you need to evaluate only one integral.

 

[n!kofeyn]

The Attempt at a Solution

i put them in terms of x and have x = 2y^2 and x = y-1.
then do i just graph it and take an integral ?

You have done the first step. Now you need to find where these two graphs intersect. You'll do this by setting 2y^2=y-1, and yes, it would help immensely to graph these two functions. I would think about graphing it in the yx-plane, that is with y being the horizontal axis and x being the vertical axis. In my opinion, this makes it easier to decide what to integrate.