Double integrals to find the volume of the solid (KristaKingMath)

[@kristakingmath]

Glad you like them! I explain the process here: integralcalc . com/how-I-create-my-videos/

[@colinposka3227]

You really have a video for every topic I have in my calc class. You're saving my grade. Thanks!

[@kristakingmath]

You're welcome, Colin, I'm so glad the videos are helping!!

[@MarkovPetar]

All of our exes have been eliminated! What a day brightener... :D

[@kristakingmath]

LOL GREAT point! I need to use that more often!! :D

[@吳擎-q5u]

Thanks a lot!! I'm a college student from Taiwan, your teaching is so nice that I wish my teacher is you. I think I will pass the final exam with your videos easily :D thank you very much! again...

[@Zayneakajordan]

This is a very Helpful Video, I was mostly stuck on the setting up the problem and this helped a lot. Thank you.

[@kristakingmath]

Awesome! I'm glad it could help. Thanks for letting me know.

[@kristakingmath]

Hey Giovanni! I'm so glad you like my videos! This is a web page I made where I explain everything I use to make my videos: integralcalc . com/how-I-create-my-videos/

[@tomctutor]

Like your Gui (blackboard) and your presentation very clear. Thankyou for illuminating a difficult double-integral= volume problem.

[@allymwashambwa3850]

I love the way you elaborate and calculate the question, thanks a lot

[@kristakingmath]

+Ally Mwashambwa You're welcome!

[@miladalbert]

Hey , Tomorrow I have Differential Equation and vectors final exam and you saved me and my friends' life. You teach better than our University's prof !!!!

[@kristakingmath]

I hope it went well! :)

[@miladalbert]

It did, You should have been our prof .... Tnx .

[@mhdwhd3442]

thanks that is really helpful. also I really appreciate what you do because you helped me in finding the volume by using washer method and cylindrical shell

[@kristakingmath]

Thanks for the comment! I'm so glad you're liking the videos! :D

[@kristakingmath]

You're welcome! I'm so glad the videos are helping! Good luck on your final exam!! :D

[@Stanley-Elo]

Is there a video on how you got the hypotenuse used for integration?

[@syalina4734]

what a great explaination ! I really love the way you explained and you did help me a lot !

[@kristakingmath]

I'm so glad it helped!

[@kristakingmath]

that equation got solved for x as x=7-3y, and became the upper limit of integration when we integrate with respect to x. so we did use it! :D

[@dhruvanshuparmar8969]

my head got fucked with this problem,and now i feel i know everything,thanks so much krista

[@debasishsingh1450]

Great explained

[@Tocket03]

I'm confused. The standard slope equation is y=mx+b, where m is slope and b is y-intercept. But I'm not seeing a y-axis intercept. Can someone explain this part?

[@Abhiabhiabhi97abhi]

A really helpful video, Krista! Thanks a lot... :-)

[@prajyot449]

great job need more lectures

[@uiticus]

Great explanation. But I wish you shaded in the volume we are trying to find here. I am having trouble picturing it. I do not understand what it means stating it lies below z=xy and above the triangle bounded by the vertices.Would that be the volume or space surrounding the triangle? Also, shouldn't the upper limit of integration for the Y integral be -1/3+7/3, since integrating the vertical slices of the triangle varies in height just like it did when integrating along the x axis?

[@mhdwhd3442]

yesterday I had a calculus ll exam which was very difficult :( and even if someone studied very hard he couldn't solve it>>>>

[@Caroline-bt6qh]

thank you very much ... you saved my semester!

[@kristakingmath]

So glad it could help! :)

[@amararyan4128]

thank u very much ma'am for this video. Plz also post some videos on tripple(volume) integrals.

[@kristakingmath]

I might just be making one next week on that! Stay tuned. :)

[@kristakingmath]

You're welcome! :)

[@noyes7196]

You are the best !!

[@giovannicapodanno4779]

Your videos are so cool! Thanks a lot for sharing all this lesson for free. May I know which software are you using to create those videos? Thanks before hand Giovanni

[@thearchitect27]

Great job!

[@kristakingmath]

+thearchitect27 Thank you!

[@mosaletswalo7764]

The quality of the audio..... 100 % !!

[@gene546]

3:00 ins't possible to use the distance formula to get the sides of the triangle or the hypotenuse? I mean, excuse my questions. Great videos.

[@anarelle]

great video! I'm a bit confused though: I've seen problems where the solid is projected on xy, xz, yz to calculate volume. Why didn't you need to project here and when do we DO need to project? An example I have is the volume of the solid constrained by x+y+z=2 and the coordinate planes. My teacher started projecting on plane xy to get line x+y=2 and went on from there...

[@michaelbardakji9824]

How did we specifically specify that the volume we're calculating is below the the plane z=x*y. What if the question was finding the volume of the solid on top of z=x*y? thank you

[@kristakingmath]

awesome!! i'm so glad the videos are helping!! :D

[@GenericMedusa99]

maybe you can draw z=xy plane, to show what does the triangle look like in the (x,y,z) axis. i thought for volume its a triple integral i.e. trip int(f x,y,z) dzda

[@Ditiro100]

What software or device are you using to make this videos.. They are very lovely?

[@allymwashambwa3850]

you are good, congratulations for you

[@kristakingmath]

+Ally Mwashambwa Thank you very much!

[@edwarddi3833]

Thanks for your video! but the idea to define the upper and lower limit is not clear. why don't you just use the x=(1,4) and y=(1,2) as the boundary?

[@edwarddi3833]

I think I have got it. ε＞

[@blackabe111]

That also confuses me haha

[@segoviapatricio]

if we get a negative volume,, what does it really mean or represent?? great video

[@kristakingmath]

it means that there's more volume below the xy-plane than above it.

[@danmcglaun1]

What is this great tool you've used to make the video!?

[@kristakingmath]

+Dan McGlaun You're probably talking about Sketchbook, or Screenflow, but here's more detail: kristakingmath (dot) com / my-videos

[@muhammedsaad3171]

can you please explain how did we get these two equations of x and y ? thank you.

[@263kk]

Equation for line y = mx + c ... Now I guess you know how to find the values of M and C in that eq. Thank you (Refer 0:50 min of Video)

[@GH123XL]

Do u have a video on triple integral? Also, I wonder why my calculus books are filled with so many trigs. What significance does it have on the calculus itself? Sorry but I really get confused. I am a self learner so feel free to say stupid on me.

[@Vk-gv3sc]

awsome videos u make...could u explain why we can't take limits of x from 1 to 4 rather than 1 to 7-3y...i mean the max value of x is 4..right?

[@Dalie3011]

because if you do it from 1 to 4, it would essentially be a rectangle. taking the limits from 1 to the line 7-3y means it's for the triangle that the vertices form

[@kristakingmath]

Awesome, thanks! :)

[@360xi]

A question. How come for x values: there is 1 and 7-3y. I would have thought the most right value is 4. Please help me.

[@kristakingmath]

yes it does. :)

[@faroukbouiche7360]

Hello thank you very much for this wonderful lessons it but I do not understand how the conclusion of the function limits of integration Palin Is it possible to help me

[@jorgeclaeyssen]

Wouldn't the outer fraction be 1/4? You took two halves yet forgot about the last one. Else, please let me know what I missed.

[@kristakingmath]

It would be 1/2 because you're factoring it out of the function. In the same way, if you had 3x-3y and you wanted to factor it, you would get 3(x-y) when you factor out the 3, not 9(x-y). I hope that helps!

[@kanivakil198]

OMG, this is the exact problem from my homework: James Stewart Calculus 8th Edition.

[@kristakingmath]

I love it when that happens! :)

[@wavoofahd7576]

Why is it that the upper limit for integration of dy is 2 not the equation of that line y=1/3...... as it is changing

[@shoes121255]

For the limits of integration with respect to the x term why is it from 1 to 7-3y instead of from 1 to 4?

[@Xylyxzs]

thought i was the only one with this hell of a doubt

[@mohem60]

shoes121255 did u figure out why??

[@Osama_Amer]

you can use 1 to 4 only if you used 1 to -1/3x+7/3

[@naifothman872]

thanks for the video , i just dont understnd where did you get x=7-3y from ? thank u

[@kristakingmath]

y=-(1/3)x+7/3 is the equation of the blue line that marks the top of the triangle. So I just solved that equation for x, like this: 3y=-x+7 and then 0=-x+7-3y and then x=+7-3y.

[@bhardiman35]

What happens when they don't give that hyp to you? I'm working on the same problem and I just don't get how you can use the vertices to find that equation of the line. I'm sure it's something simple but it's escaping me now.

[@kristakingmath]

You use the point-slope formula for the equation of a line, y-(y_1)=m(x-(x_1)). You find the slope as (1-2)/(4-1)=-1/3. The slope goes in for m. And one of the points goes in for (x_1,y_1). So for example y-(y_1)=m(x-(x_1)) becomes y-2=(-1/3)(x-1), so y-2=(-1/3)(x)+1/3, so y=(-1/3)(x)+1/3+2, so y=(-1/3)(x)+7/3.

[@badriaibrahim9918]

Thankyou so much ❤️

[@kristakingmath]

+Badria Ibrahim You're welcome!

[@mohamedharedi8437]

thanks a lot

[@EpicMicky300]

how did you get the equation for your lines?

[@CaptainFluffen]

The upper point of a line is (x1,y1) the lower point is (x0,y0). Calculate the slope m=(y1-y0 / x1-x0) then plug it into y-y1=m*(x-x1) and isolate the y on the left side and the rest on the right.

[@zandiviljoen146]

YAAY was looking for this specific sum coz I kept getting the same wrong answer, turns out i forgot to write the second limit as the equation of the line and just wrote it as the max y or x value lol oops.. thank you ma'am!!:)

[@kristakingmath]

You're welcome, Zandi, I'm so glad it helped! :D

[@randycarr5869]

The Algebra part of finding the upper and lower limits is understandable.... but why is the x upper limit not 4 as opposed to using 7-3y......the lowers being 1 makes sense, and the upper for the y value being 2 makes sense.....so why isnt the upper for x equal to 4???

[@kristakingmath]

Because depending on which y-value you pick, the upper limit for x will change. If you pick y=1, then the upper value for x is 4, but if you pick y=2, then the upper value for x is 1. So because that value is changing along the slanted line given by x=7-3y, you have to use 7-3y as the upper limit. :)

[@randycarr5869]

why doesnt the same equation serve as the upper limit for y as well.....does it not bound the vertical boxes when respecting y, as does it bound the horizontal boxes when dealing in respect to x????

[@Electric301]

Is this triangle on the xy plane? How do you know

[@hahakun96]

can you please please please show how to find the upper limit when the lower limit and area are given? I am stuck at it! >n

[@modibacm2783]

How did you come up with those two equations for x and y

[@frederickben-smith990]

find the volume lying the sphere x^2+y^2+z^2=4z and inside the paraboloid z=x^2+y^2 pls can you solve for me

[@dhirajojha2853]

hi can i please know where/how did you get the values for y=(-1/3)x=(7/3) and value of x too...thnx

[@bobolecoq2599]

you just need to use the formula of the equation of a line passing by 2 points, in this case the two points being (1,2) and (4,1). and the formula is y-y1 = [(y2-y1)/(x2-x1)](x-x1)

[@dhirajojha2853]

Thnxs +Sam dhena

[@GH123XL]

sorry but does xy there mean x times y?

[@makwaruzomohamed2067]

i do appreciate.. ..thank you

[@kristakingmath]

You're welcome!

[@jamesmoriaty1098]

Love u krista

[@0011mim]

I dont understand how do we find the hypotenuse :(

[@HG-lr7lv]

We are given the points (4,1) and (1,2). To find the slope: (2-1) / (1-4) Here we obtain y = (-1/3)x Now, to find the 7/3 that she has for her hypotenuse equation, we take the highest 'y' value, which is 2, from the given point (1,2), we add (1/3) (the slope) to 2 because we want to obtain the y-intercept. We finally obtain y = (-1/3)x + 2 + (1/3), which equals y = (-1/3)x + (7/3)

[@ningxinyang6713]

why is the upper bound for the inner integral 7-3y rather than 4?

[@kristakingmath]

Because the upper bound for x is only 4 at y=1. When y is greater than 1, the upper bound for x is found along the line x=7-3y. Since the upper bound for x varies, you have to make it 7-3y, not just 4.

[@ningxinyang6713]

thanks so much :) keep up the great work!!!

[@حسينعلي-و4ج9ص]

thanks you 🌷🌷🌷💖😘💖🌷🌷🌷

[@kristakingmath]

You're welcome!

[@gilbertosimango5739]

how to get the formula of the y and x from the graphy?

[@canveahmetkayacan]

from the Two Point known line equation , y-y2/x-x2 equals y2-y1/x2-x1

[@kristakingmath]

:)

[@IfautahSkimm]

I feel math people make the examples really easy and convenient to themselves. Solve something involving extra variables (h,a) or something which is not a perfect shape! What happens if there is not discernible minimum or maximum. I am tired of seeing the same examples over and over which don't help me solve the problem I have on hand. There is no need for 700 videos explaining how to find the volume of a simple geometrical figure with an extremely convenient function which won't appear on any test or homework EVER!

[@duongchankhuon5404]

Hi sister

[@obadaali3686]

i love u

[@CamiloSanchez1979]

Smartest chick on the internet. Wow

[@TheeEnd23]

Marry me

[@obadaali3686]

can i married u

[@ashwinsharma3720]

99 percent Students visiting Channel are men .That's why they say men will bei men 😂😂

[@joeltshite5279]

hey Krista, you are cute