Area between curves; Both dx and dy Integration

We practice setting up the definite integrals required to find the area of the region bounded by two functions. We set up definite integrals with respect to both x and y. The functions are given to us as functions of x, y=x^2 and y = 2-x. In the first segment of the video, we rewrite the equations of the curves as functions of y which will allow us to integrate with respect to y. In the second segment of the video, we set up the dx definite integral that would give the area of the region, subtracting the top function minus the bottom. In the third segment of the video, we set up the dy definite integrals that would give the area of the region, subtracting the right function minus the left. In each case, we discuss the orientation of the representative rectangle. We do not evaluate the integrals.

[morganmandaro]

The first video that covers a problem like mine that I could not figure out. Textbook had no examples like this and neither did my lectures. Thank you for this now I understand!

[stephanieguevara]

1) Stephanie Guevara
2)Monday and Wednesday 11 am-1:15 pm
3) I learned how to be able to find the area by two bounded functions by first separating it into two functions of y so i can be easier. There are two ways to work it, integrating it respect to x and integrating it respect to y.

[mrTechdecker]

Random student from a different college. This video helped me figure out how to decide whether it is only one integral or two integrals to find the area in terms of x and y. Thank you again as I struggled the past two days!

[nicolehovorkova]

Nicole Hovorkova, MW11-1:15
I have just learned how to solve an area between two graphs with respect to y. I never thought of it, wonder if there is actually some significant preference/ easiness in choosing one over the other. So with respect to x we do top-bottom, but with respect to y we do right-left. Noted!

[einoaction]

Love your voice and simple explanations....math made eazy

[gabriellebateman]

Gabrielle Bateman
MAC2311
One thing I liked about this video was the fact that it showed how to set up the integrals and find the equations based on "y". Sometimes, we are so quick to solve such equations based on what we have practiced before. It is important to stop and analyze the graph, what is the graph showing?

[gaberodriguez]

1) Gabriel Rodriguez
2) MoWe 11:00am-1:15
3) I learned that to set up the dy you have to set up two separate integrals because you have to use two separate formulas based on the location of the rectangles.

[jasonkildare]

Jason K
MAC2312
One takeaway from this video is understanding how to find the area between two curves using dx and dy integration.
This video helped me understand ways to integrate each function. Integrating dy, we will subtract the functions right to left. For dx, we will subtract the top function from the bottom.
Thanks, Ms. Hearn.

[sheercold]

Hello Ms. Hearn! I thought of trying to get the area with dy integrals. The biggest take-away from this is that there are different situations where either using the dx or dy integral would be better. If the dy integral crosses over multiple curves, for example, it may be a better idea to use dx instead.

[brancoforti]

Branco Forti
MAC2312



I learned how to set up definite integrals to find the area of the region bounded by two curves, both with respect to \(x\) and \(y\).

One take-away from this video is the importance of properly identifying and setting up the integrals based on the orientation of the representative rectangles, which ensures accurate calculation of the bounded area.

The video helped me understand the process of transforming functions between variables \(x\) and \(y\) to set up integrals correctly, which is crucial for calculating areas between curves.

[danielcorrea]

Daniel Correa
MAC 2312 Tues/Thurs 1pm-3:50pm
After viewing this before our midterm, this video really did help me when it came to representative rectangles. I see why they are important to draw and based on the axis of rotation you will be able to see whether or not you will use the disk or shell method.

[kaelarose]

1. Kaela Joseph
2. MAC2311: M/W 11-1:15
3. In this video, I learned that integration with respect to x and y is necessary to solve the problem and I also learned how to go about those methods.

[jfryer]

Wouldnt it be simpler to integrate between the intersect points and take this away from the area of the trapezium calculated without calculus?
I didn’t find an answer and was confused with so many integrals in both x and y which seem to make the problem far too complex.

[robertogarrido]

Roberto Garrido
MTWR 12:30 MAC2311
0:20 Before you start setting up the integrals if we know that we're going to have to integrate once with respect to x and once with respect to y that means it will result in 2 equations where y=something and x=something.

[williammatiz]

William Steven Matiz
Monday/Wednesday, 11AM-1:15PM


I kept messing up on this problem earlier on my homework, and I finally realized my mistake. When I was setting up my integral, I did not subtract the x^2 in the argument. I think I thought originally that the entire graph was just one graph. I see now that since those are two different functions, those are 2 separates graphs, and you have to account for that when setting up an integral.

[leonardoyasbec]

Leo Yasbec: Mon, Wed at 11am-1:15pm
I learned how to separate the graph when you have x equals positive and negative square root of y, and how to find the dy with integration. Specifically how to get the values for the integrals by testing them by plugging in x to get the y value.

[edisondelmoral]

Edison Del Moral
MAC2312
One important note from this video is that sometimes it is possible to do either a dy integration or a dx integration but the bounds will differ and depending on the given equations it may be necessary to convert from an equation which states what x is equal to in terms of y or vice versa.

[harshdwivedi]

Your video is awesome it helped me a lot . Please continue your work

[jonathanschnoor]

Jonathan Schnoor
Mac2312
I learned that for a dix problem, you do the top function minus the bottom function. For a dy, you do the right minus the left

[ec]

1. Enrique C
2, M/W 11-1:15
3. Recognizing which is the top and bottom function as well as the points of intersection. This would help set up the integral