Area between curves... which curve is which?

► My Applications of Integrals course: www.kristakingmath.com/applic...
When you’re doing an area between curves problem, one of the toughest parts of the problem is figuring out the orientation of the curves. And that part is actually the crux of the whole area between curves problem. Whenever you’re doing an area between curves problem, you always start by figuring out the intersection points, which is really simple because all you have to do is set the curves equal to each other. And you always finish off the problem by setting up the integral that represents the area between the curves. But once you’ve got that integral set up, you’re really home-free for the rest of the problem, because all you have to do from that point is evaluate the integral. The critical middle part is figuring out the orientation of the curves in and around those intersection points, because once you know the orientation, you can easily set up the integral.
So how do you figure out the orientation of the curves? Meaning, how do you figure out which curves is on the top and which is on the bottom, or which curve is on the right and which is on the left? The good news is that figuring out the orientation of the curves is actually not too difficult. All you need to do is pick a point on each interval (between the intersection points and/or the given endpoints of the interval), and evaluate both curves at that point. Whichever curve returns the larger value is the curve on the top. Or in the case of left-right oriented curves, whichever curve returns the larger value is the curve on the right.
Once you’ve got the orientation figured up, then you want to set up your integrand as (top curve - bottom curve), or (right curve - left curve).
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
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[@amandaclark73]

Such a straightforward explanation --I had such a hard time finding any explanation of how to approach the problems only algebraically without graphing the curves. Easiest to understand areas between curves content I have found. Thank you so much!

[@kristakingmath]

You're welcome, Amanda! I'm so glad this helped you with the algebra approach... we definitely don't want to have to graph every curve! :D

[@soliscrown1272]

Very good explanation!

[@aakashshaw]

It was really very much helpful ❤ Lots of respect to you. ☺

[@lamooh7008]

thank you so much!!! i was so confused but this helped a ton :))

[@StreuB1]

I am utterly failing Calc1 at this point but I still view it as a success because in December, none of this would have made sense AT all. And while I do not know how to do integration yet, I understand every aspect of this as well as knew how to do some portions, before it was talked about. It was already apparent to me. So, I think that is still a success. Thank you for the great videos, Krista!!! Withdrawing and then retaking a class isn't failure, its a success when you realize your shortcomings ahead of time and stick with it long enough to get as much out of the class, but withdraw in time to not fail the class. :-) That being said, I will be retaking Calc1 over the summer and giving it 110% again. I WILL GET THIS AND BE GOOD AT IT! :-D

[@1972hattrick]

what part of calculus gives you the most trouble?

[@kristakingmath]

Yes you will! Love your attitude, Brian... You'll be past this hurdle before you know it! :)

[@ankitbisht7]

nice job

[@ILikeReadingTho]

Thank you very MUCH!!!

[@kristakingmath]

Glad it could help! :D

[@aklile_ag]

We have missed you!❤

[@kamvc72]

I bought her course on udemy , it was very helpful, i got enlightend like never before.

[@alwysrite]

very well explained

[@kristakingmath]

Thanks!

[@w1ndro1d]

I liked just because of your voice!👍 Awesome girl.

[@christophermalecki9772]

ooof.

[@jeddaaah]

what kind of software you are using? i like it alot

[@lekirie]

Hello, Krista! What if the given is y = (1-cosx)(sinx), how do you find its integrated value?

[@leocheng9428]

thank you

[@kristakingmath]

You're welcome! :)

[@bhagatcharan1127]

nice one sister

[@lilya553]

How about if we have functions like y=cosx, y=cos^2x on [-pi,pi]?

[@mogdor]

I failed calculus three times. Damn ADD.

[@Oggy-kun]

thanks

[@kristakingmath]

You're welcome, Bobby! :)

[@vrendus522]

I really like this partilar format for some reason. I did not like the place the plug-in videos, as for some reason they were irritating. But on this vid, I really like it. I was born dyslexic, but learned to pilot around this is life, so a lot of times I will get the answer even before the math work, so in these videos, you seem to make things easier. You have an extremely likable personality, Krista. I swear that you could dress up in a Barney The Dinosaur suit, give a lesson and everybody would still get it. Thanks, very good video. -Liked this particular video, as in a way it deals with a problem on hidden potential volumes as well as matrices irregular surfaces. So this process is valuable to know if you must formulate unknowns, in modeling CAM CAM design display engineering problems.*It is vitally important to be able to realize this process within your own head, that's why is vital to be able to visualize the math, as you do for us here. Has to become a second instinct.

[@kristakingmath]

Thanks, I'm so glad you liked the video! :D

[@christophermalecki9772]

I am walking into a calc final in like an hour and I could not find a single video or article that explains how to figure out which curve is the top one in an interval where it switches. thank you

[@kristakingmath]

I hope the final went great!! :D

[@afrozabegum9935]

💛

[@craig7878]

Hi! Can you please help me? Given f(x) = x^2-5x+6 and g(x)=-9x+18, I calculated intersection occurs at x = 2 and x = -6. I looked at graph, and i think my upper bound is -6 and lower is 2. Is that correct? I calculated the area to be -256/3, but i think it should really be positive because area is positive, so i let it be positive. Is that correct?

[@ZmMathClasses]

Very nice classes😅😅

[@user-mq4qj2bl7g]

This application for integration?

[@manjunathneelmath2104]

Very nice explanation. Are you a Professor?

[@kristakingmath]

Thank you! No, I work full time on my own online courses! :)

[@thomasrua57]

I love you

[@kristakingmath]

[@sjt62349]

you proved that f is top and g is bottom at x=2 only, which doesn't say much, but otherwise very nice.

[@jackibackiboy5528]

In fact, it actually does. By finding the intersection points of x=0 and x=4, we know for a fact that no further intersections will occur in the interval ]0, 4[. Thus, one of the curves MUST be situated over the other curve for all values of x inside this interval. That means that we can pick any value for x such that 0 < x < 4. Hope this helps!

[@AliHassan-hb1bn]

f(4) is not a curve baby, it is constant line

[@kimvarela9895]

this makes no sense to me.....

[@kadekevin566]

good one on a side note: shouldn't your name be Krista Queen?

[@jameeltheprince]

Why would it ever matter as which curve is top or bottom? Integrate it and take modulus of the answer. Simple.