Double Integral Using Polar Coordinates - Part 1 of 3

[SecureOpsWizard]

This video was made 9 years ago and it's coming tremendously useful to me today. Thank you Sir for what you do.

[carlhenry]

I owe my engineering degree to you sir...well at least half of it lol

[arnolddrummer]

You my friend have helped thousands of science/engineering/finance students understand Calculus. With any luck, much fortune will come your way.

[dimitrismezes]

you're the secret superhero of everyone's math exams :P

[obliquecolumn]

The r term in the equation at 2:33 on the video, comes from substituting x^2 + y^2 = r^2 on the left hand side. And on the right hand side, y/r = sin(theta) so y = r x sin(theta), which is substituted on the right hand side.

[JimCharlesTroy]

Patrick, dude, I'm completely sure that God's got a special place reserved just for you. You are awesome and from the bottom of my heart: Thank You.

[patrickjmt]

yes, a good graph goes a long ways in helping...

[cheahyewtan]

i understood the whole thing in just 5 mins .... where my lecturer took 2 hours and i get nothing ....

[claugi]

out of all the people that submit videos with lectures, you are my favorite. thank you so much for sharing your knowledge and expertise.!

[AndrewSouthworth]

When going to polar coordinates it is required.

For example, we need an infinitesimal change in the area of the shape. To do this, we multiply a small change in r, by a small change in arc length. This arc length is equal to r*theta, coming from basic trig, and the infinitesimal arc length would be r * dtheta. So when changing to polar coordinates it becomes r dr dtheta.

[Luwawa]

Partick u've saved me, jusr have an exam 2morrow n from 5 days i couldn't understand this matter, thank u dude keep doing this u'll save thousands student's life..thanks from an Angolan in Poland :)

[dgmm]

i wish that make ur videos as the book titles and organize them the same to book too :)
as a lessons .. thank you are a great man .. very helpfull ..

[hyphend]

This now 15 year old video is still invaluable today. Thank you for making this, and I hope whoever made this is doing well!

[KleinGrass]

Why is theta between 0 and pi and not between 0 and 2pi if it's a full circle?

[TanaySingh]

You just cleared this concept for me in 2 mins which my uni couldn't in 2 full days of classes....

thanks a bunch mate!!!!

[bfgamestotal]

man, your channel is just incredible .. i am giving up MIT classes and joying PJMT lololololol

[samueln]

And after 13 years your video helps me to pass math exam, God bless you!

[liverpoolfans]

thanx patrick..i`ll be sitting for my math exam and this vid has been really helpful..

[mariapersaud]

I'M GONNA PASS MY QUIZ BECAUSE OF YOU

[muscleman]

@patrickJMT well just looking at the circle one can see that since its not at the origin it cant be 0 to 2pi, its above the x axis and that region is 0 to pi