Area between curves - dy (KristaKingMath)

► My Applications of Integrals course: www.kristaking...
Learn how to find the area bounded by two curves. In this example, the curves are defined for x in terms of y, and you'll integrate with respect to y.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
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?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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[@claytonmarquardt5522]

i love how slowly and simply you explained that, it was incredibly helpful. thanks a bunch!

[@kristakingmath]

+Clayton Marquardt I always hated when we had to move too quickly through the material, so I try not to do the same.

[@lolipopscandy62]

You are literally an angel...there's just no other way!

[@raejohnson2647]

Thank you. I had this exact problem in my Calc 1 class.

[@seadiver021]

Hey just wanted to say thanks a bunch for posting such amazing videos!! You are honestly the only reason I passed calculus this semester [= now i must get through calc two and physics next semester =\ stay awesome!

[@arbiter320]

MAN thank you so much for this video! You've explained a concept in 7 minutes, where I couldn't seem to grasp the idea in a lecture that is over an hour! Again, thank you very much!! Subscribed for Past, current, and future content :)

[@kristakingmath]

:D

[@PandaG0419]

This is kind of irrelevant but I have to say that u have such a sweet voice...makes watching these videos even better

[@KMURRA]

Thank you again so much for this video, you always seem to post videos of what I'm going to be tested on, thank you for your time!!!! Truly appreciate it.

[@haugvision]

I love the way this girl teaches calculus.

[@tanvirazad49]

You're a life saver... I am bad in expressing gratitudes.. but thanks a bunch!

[@kristakingmath]

+TnV You're welcome, I'm glad it helped!!

[@ohok5970]

Jason Meyler You have 2y^2 on one side and 4+y^2 on the other side. 2y^2 means there is two y^2. If you were to subtract one y^2 on both sides you would have 1y^2 = 4 left. (or y^2 = 4)

[@Ensign_Cthulhu]

It occurred to me at about 3:12 that both of these functions are even about the X axis, first by observation and then by subbing y and -y to check the x value. So the integral could be taken from 0 to 2 and its value doubled, which makes the maths easier... for polynomials like this, the entire expression vanishes at the lower, zero bound and you only have to sub in for the upper (and do the doubling in this case) and your answer immediately appears.

[@tommylee2721]

I can't stop thinking about your beautiful voice!!

[@ChocolateMilk19]

Taking Calc 2 rn your vids are 👌

[@husame38]

thank you for all your videos

[@elizabethsamura5590]

you are awesome!!!!!

[@davidferna93]

Loving the color of the board, please keep it that way :)

[@kristakingmath]

That's awesome!! I'm so glad they helped!! :D

[@kristakingmath]

Glad I could help!

[@frostpistol]

I have to send my teacher to u to teach him how to teach. Great video and thanks

[@kristakingmath]

I'm sorry to hear about your teacher, but I'm glad I can help! :)

[@jose95ruiz]

So helpful!

[@kristakingmath]

You're going to rock calc two and physics! :)

[@user-qu4ky4eg5g]

Possible give us lessons in the conversion of the decimal system to binary system and vice versa

[@kristakingmath]

You're welcome!

[@ryanmorris7473]

I don't know if its just me but shoudnt the integrand have 4 + y^2 instead of 4 - y^2? Is it just a translation error?

[@ryanmorris7473]

I see that you combined both equations as one algebraic expression and then integrated, ive taken calculus I, so I don't know the rules for these new problem types so I trust you and thank you for such amazing teaching, do you work as a calculus teacher in a college or university?

[@kristakingmath]

+Ryan Morris I was a tutor for a long time, and now I do this full-time! :)

[@OverLordOfDa3rdWorld]

GOD BLESS YOU, LADY!

[@sulaimanahsan6651]

I love you .......it just very helpful during quiz ....love u soo much

[@kristakingmath]

Glad I could help! :D

[@kristakingmath]

Thanks!

[@OmarHiweish]

Thank you soooo much, that was very helpful!

[@93ksj]

I really like this topic ;D Thank you once again!

[@kristakingmath]

You're welcome! :D

[@MajidFalehx2010xMMM]

Thanks a lot

[@java4235]

thank you for your videos. You are very helpful

[@kristakingmath]

You're welcome!

[@forzatony]

your very helpful thanks alot

[@mf2709]

THANK YOU THANK YOU THANK YOU

[@anadiru4382]

Quick question, u integrated the first function 4-y^2 but u didn't subtract the integration of the second function 2y^2. am I missing something?

[@shazienea2749]

Thank you So Much

[@kristakingmath]

I wish some of these tools were available sooner as well! :)

[@MsReeses97]

do you only put the +C when you have an indefinite integral?

[@kristakingmath]

yep! :)

[@jasonmeyler7205]

In the beginning of the video @ 1:01 you subtract y from both sides and getting an answer y^2= 4. How did you get that?

[@hopefulee8402]

+Jason Meyler 2y^2-y^2 = y^2

[@kangemanmaipmokiuah226]

thanks

[@hopefulee8402]

Is there a method I can use to graph these x= equations on my TI-83 calculator?

[@debbietan114]

Tq very much

[@kristakingmath]

thank you!!! :D

[@OnlineEducation8375]

Good explanation. Which software are you using for writing?

[@kristakingmath]

Thanks! I use Sketchbook (by Autodesk). :)

[@Cmweinburger]

Hello, What brought me here is a quick question... How do we know when to integrate with respect to DY instead of DX?

[@kristakingmath]

If your curves look like they're on top of each other such that you could call one the "upper" curve and one the "lower" curve, and you can draw vertical rectangles to approximate the whole area, then you need to integrate with respect to x. If your curves look like they're next to each other such that you could call one the "right" curve and one the "left" curve, and you can draw horizontal rectangles to approximate the whole area, then you need to integrate with respect to y. :)

[@Cmweinburger]

Wow. Thank you so much! Your response was very informative and helpful.

[@mrboyban]

I love you!

[@fancy_pixel]

i have a stupid question but why is there is no +c in the end?

[@kristakingmath]

+fancy pixel That's not a stupid question. The reason is because it's a definite integral, which means there's an upper and lower limit of integration, and whenever that's the case, you don't add the +C.

[@kristakingmath]

Aww thanks! :)

[@jerzydude94]

Do you have heterochromia? Looks awesome.

[@RafaSyed]

Is there any playlist containing related problems to this?

[@kristakingmath]

The third, fourth and fifth videos in this playlist are all area between curves problems: kzbin.info/aero/PLJ8OrXpbC-BMz4irMey8DcJe_iiXgA9aI

[@kristakingmath]

I like it better too. :)

[@kristakingmath]

I must just have that sixth sense or something. :)

[@johnparks6936]

I'm having trouble drawing the graphs when the function is in terms of y. Can someone please explain the process behind that?

[@kristakingmath]

+John Parks Hey John, to sketch a curve that's in terms of y, you could plot individual coordinate points and then connect them. For example, plug in 0 for y, and see what x value(s) you get back, then plug in 1 for y and see what x value(s) you get back. Or you could flip the variable and sketch the curve as if it were the normal y=...x..., and then reflect that curve over the line y=x. Either method will give you the graph of the curve x=...y...

[@johnparks6936]

CalculusExpert.com Thank you so much, I'll give that a try!

[@akuraoo]

What software are you using, please?

[@skategenie]

You're amazing

[@kristakingmath]

I explain here :) integralcalc . com/how-I-create-my-videos/

[@kristakingmath]

Ya I don't think KZbin always give 100% accurate view counts

[@gjangir8381]

Thanks but give shortcut methods.

[@user-mm3rt7cw5t]

i love u

[@Xavior12]

Your view count also says 3? weird, me too...

[@ThePinoyMamba]

:)

[@juliendark4208]

mARRY ME PLEASE!

[@kristakingmath]

Aww thanks! :)