Area under the parametric curve (KristaKingMath)

Learn how to find the area under the parametric curve and above the x-axis.

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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?!”

[nkazinchinda]

Hi, I'm a sophomore who is going for valedicatorian, so I took the AP Calc BC Exam this year while taking the AP Calc AB class. I got a 5 on both portions, and if it wasn't for my six hour integralCALC youtube video marathon the weekend before the exam, I would have been lucky to get a four! Thank you so much!

[caseykc]

Your voice is so soothing, even people who don't like math can watch your videos all day long. You explain everything very well, I wish you were my professor. Thank you for these videos.

[westaylor]

It is amazing how clear you can explain it! I go to class I listen for content and ideas then I come here for the explanation. You are awesome!

[jitterball]

You have the softest voice ever! If you were my teacher, you'd always find me sleeping during your class^^

[MrCrazyGuy]

we did all this work to arrive at 3-e i should have become an art major but im in calc 3 no going back now lol

[andresb]

Krista you are an awesome youtuber it is a crystal clear explanation or "Kristal clear" lol thank you so much, I do not have enough words to thank you for all that I've learned with your videos. God bless you!!!. 😊😊😊

[ChristopherMendoza]

You uploaded this right as I needed to learn it. Thanks so much! :)

[kristakingmath]

love it when that happens! you're welcome! :)

[airshw]

Hey great explanation and your videos have been really helpful to me but I may suggest a revision to the method of finding the limits of integration. Instead of eliminating the parameter. I suggest just solving the parametric equations for the parameter by solving the y parametric equation for zero then plugging those values into the x parametric equation to get the 1 and zero for t and it is much easier.

[Pluxars]

Isn't it much easier if you start out setting y=0 then it gives you the t values 0 and 1. You know the y component is 0 then you plug the t values into the x equation and you have the coords on the x axis. You can pick 1/2 t to make sure that it is concave down. Then you never have to get into natural log and it seems to be much simpler.

[kristakingmath]

thank you so much, i'm glad you think so!! :D

[jorgerangel]

I really love the way you explain, thanks you!.

[deepakbharti]

The way to explain things is awsome ... you magiclay make things so easy... :) great work !!! carry on... :)

[Quijanos]

Superlative job! Love the voice and explanation.

[Pluxars]

I meant to say that your video was also very helpful! Thank you!

[Falcon]

Very helpful, thank you!
What's the extra benefit from using your website rather than just watching the videos on YouTube?

[StandbytheTruth]

I think it would've been nice if you had explained why the x values after eliminating the parameter give you your a and b. It's not obvious at all why they are the limits of integration. Also, since our curve is above the x-axis, this implies that y>0 which means that as another person said, I could've found t=0 and t=1 and then do a sign chart which would've given us the interval from t=0 to t=1 that works which then we could proceed to solve our parametric integral.

[chancekelly]

I love your explanation! Thank you sooo much! 😊

[robertcoggin]

One thing that keeps tripping me up is my book has integral set ups for area under parametric curves where either f(x) or g(x)'s derivative is used, depending on whether the curve traces out clockwise or counterclockwise. Is this merely determined based on the points of x and y you'd plot for the values of t found from alpha to beta? The book is terrible at explaining this and only mentions it in one brief block before moving on, but my homework problems have been in question on account of this.

[DOLrd]

This video is fucking spectacular. Stewart Calc, 10.2, # 33.
I had a lot of trouble with this.
I never thought to factor out the ln(x-1) to leave [ln(x-1)][1-ln(x-1)]. I had tried doing this without factoring and it was a bit more difficult that way.

As long as you keep picking out the tricky problems in the book and explaining them, I will keep watching.

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