Setting up a Double Integral Using Both Orders of Integration
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- čas přidán 5. 08. 2024
- This videos shows the setup of 3 double integrals using both orders of integration. Two are bounded by curves and the third example is a triangular region.
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the is the clearest example on the internet. this video should be recommended first.
Exactly what I needed, efficient and straight to the point. Also, a MASSIVE thank you for the closed captions!
Clearest and best examples on youtube. Thanks for all the hard work you do.
This was great. I'm taking two different classes that use this stuff, and both classes just kind of brushed over it. It's really helpful to spend even just 10 minutes going through examples. THANK YOU!
Loved the last example in particular! You're awesome!
Thank you! My professor didn't elaborate how we had to go from left to right when obtaining the lower and higher bounds of the integral with respect to x. It explains a lot, thanks!
Thank you, darling! That is just the kind of knowledge and detail that I need for my studies. You're the best!
I yook your online classes at Phoenix College for Calc I-III. I am now a senior EE student at ASU and just want to say that your videos are still the best reference material for when I need to refresh on Calculus topics. Thank you!
Congratulations! I appreciate you for taking the time to comment. I happy to hear you are doing so well.
the best one explaining double integral, goat
Than you!
Actually from 0 to 1, y=x^3 would be below y=x^2. If we consider x=1/2
(1/2)^3 = 1/8 and (1/2)^2 = 1/4. 1/8 is less than 1/4 so y=x^3 would be below y=x^2. I hope that makes sense. However, after x = 1, y=x^3 would be above y = x^2. I'm glad you find the videos helpful!
You, my friend, are awesome. Thank you.
Thank you for helping me understand this aspect of multivariate calculus
oh yeah, this is what i've been looking for. thank you.
Thank you so much this really helped me a lot!
Liked and subscribed. Very efficient and well organized thought.
Thanks, this was so helpful.
Been looking for this kind of explanation, thank you for this,
I am glad I could help.
Hey there! What if the problem gives a region but not a explicit function to use (like f(x,y)=(x+y))?
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Exactly what I needed.
Thanks.. Its very helpful...
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Wonderful! Thank u very much!
when you changed the integration how did you see that sq root of y is the lower limit . your graph did not change? am very confused please help
thanks
I get that this a 9 year old question, but for anyone else with confusion about this, I'll try to explain it using the first example in the video.
When initially integrating with respect to y first, you can clearly see that within the region, the y limits should be from the lower function to the higher function (x cubed to x squared). When he changed the order of integration such that we integrate with respect to x first, you need to think of lower to higher as left to right instead of bottom to top. Also, since he's now integrating with respect to x first, the limit needs to be such that x = the limit. Looking at the graph, it's obviously not very clear which function is further to the left when you're near the origin, but if you draw the little rectangles as he did in the video, you will clearly see that y = x^2 is further to the left than y = x^3, so after setting both of those function equal to x, you end up with a lower limit of y^(1/2) to the higher limit y^(1/3).
omg, so helpful
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You mislabeled the graphs. y= x^2 is the outside curve, not the inside curve. Remember the graph of x^3 increases faster than the y= x^2 graph so it is more narrow.
I love your videos, and thanks a million for them.
You are incorrect, he did not mislabel the graph. The graph is showing each function between (0, 0) and (1, 1). Every single x value that isn't tied to an intersection point is on the interval
0 < x < 1. For every possible x value on that interval, the result of (x)(x) will be greater than the result of (x)(x)(x).
Example: x = 1/2
f(1/2) = y = x^2 = (1/2)(1/2) = 1/4
g(1/2) = y = x^3 = (1/2)(1/2)(1/2) = 1/8
1/4 > 1/8
This. One can also consider the auxiliary function
g(x) = x^3 - x^2 = x^2(x-1)
on the interval (0,1) to explicitly see the which is the majorant function in this set.
He sounds like the voice translation box Finn and Jake got for Lady Rainicorn so Finn could understand her but it only worked in old man mode
Why not from -1 to 0 plus 0 to 1?
Bro that verse she just quoted is from Al Anfal, which is literally talking about the battle of Badr, where Pagans. Brought their army to medina to slaughter Muslims, that verse is referring to them (specifically Quraysh), not innocent people. Quraysh had been slaughtering and oppressing them for decades.
The verse is merely reminding them of their enemies and to continue fighting them as they have initiated an attack on the Muslims.
Lying is not a good habit. Read with an open mind next time and don’t pull verses out of context and read the whole chapter and understand it’s context if you’re going to make a judgement.
The quote of the Americans saying “kill the japs” from WW2 isn’t applicable to present time, and it would be a dumb statement to say it would apply towards japans civilians in 2024.
Also btw this video was pulled from Ali Dawahs channel, where he refuted her interpretation of the verse with the context, but she ran away 😂