Multiple Integrals 6: Limits of Region R (Type II)

[browno26]

weeeeeeeeeeeeeeeeeeeeeeeeee

[browno26]

hooray



[isam1335]

Dude how to sketch the function and find the region? =( that's crucial before determining the limits...help me please =(

[dosyjenks]

thank you, that was such a help!! x

[Losuol]

Did he say high school? Holy shit!

[DeluxeWarPlaya]

@Losuol yeah, western high school is so far behind Asian countries.

[zayed123123]

hello dony,

my concern is how to find whether it is a "type 1" or "type 2" integral ?

thankyou for your efforts...

:)

[anujjuneja1]

@zayed123123

Just check out for the limits...if limits are in term of x, it will be type 2, which i think he mention in 4th lecture if i m right...

Just simply see, if the variable in limits(limits are in terms of x or y), then integrate 1st wrt other variable...I hope its helpful...

[DeluxeWarPlaya]

@anujjuneja1 It is easier to realise that for a dy integral, the limits must be y=f(x) and similarly for a dx integral the limits must be x=g(y). That is how my maths professor taught me. Then just make sure you have the constants on the outer integral to ensure that the final value is a scalar, not a function of some other variable.

[anujjuneja1]

@DeluxeWarPlaya

Thats wt I means...:)

[wizsoft]

Thankyou Dony, you really demystify multiple integrals. I can see that the differentiating between Region types I & II will will largely be irrelevant when you understand the mechanics. I am now fearful on not constant regions in volumes!

[eleynasr]

shouldn't that be 2y^2-2y^3 and not 3y^3? subsequently i get to -36 rather than -68! am i the one who's wrong?

[Joyfulkilla]

I keep thinking it shoudl be y=0 instead of 1 cause thats where they are equal to each other. I"m I wrong? If so how did u get y=1.

[Daljo681]

Equations y=-x+1 and y=x+1 imply that both of them edge the y-axis. y=kx+m where the m is 1

[Vidrinskas]

Hmmm. Very good exposition indeed. Maybe you could do with a bigger board though lol. Do you cover the case when R is a triangle with no side parallel to the x or y axis?

I tend to move around a lot too :)

[UntoldWisdom1]

Nice video, but the intergration was wrong. However, its good that someone previously caught that error. Keep up the good work.

[jimmyshitbags]

i wonder what happens when R hasnt got any flat sides... i'll have to keep watching...

[donylee]

Yup, good question. I see that you are thinking ahead.

A simple answer is that our regions or R are limited to type I and type II, when either the top and bottom, or left and right are bounded by straight lines. I did mention earlier is that plane regions can take a variety of forms and this is why FOR NOW, we will restrict ourselves to simple ones.

The most complicated region we'll deal with is a circle.

[imafknninja]

Hey Donny, excellent videos, you're a great instructor. However, I have a question over the example in this video. You give the answer to the inside integral as 2y^2 - 3y^3, but after several tries, I keep getting it as 2y^2 - 2y^3, and the final answer as -26/3. I'm giving you the benefit of the doubt, since you're much (much much much) better at math than I am, but I'm still unsure where the mistake could be. Would you be willing to do a quick re-check to make sure you had it right?

[donylee]

Hello imafknninja,

Yup, you are indeed right. The result of the inner integral is 2y^2 - 2y^3. However, the final answer is still -68/3 after integrating 2y^2 - 2y^3 wrt to y from 1 to 3.

I think you missed out either one of the coefficients from y^2 or y^3 term.

[LongShlong125]

So basically in the inner limits it all comes up to the g2 and g1 functions in terms of the var in the outer integral so it gets wiped.

a good explanation as always and you are probably the first on YT to give such a complete set of lessons , so big props to you yet again.

[facevokk]

wow, you sure like to move around a lot.

[donylee]

Haha, I'll do whatever it takes to grab the viewer's attention!