Session 10: How to solve Double integrals problem using Polar Coordinates. Concept and examples.

In this video, we will see how double integration problems can be solved using Polar coordinates. We will see that whenever we have curves in the questions then using polar things become very much simple.

[@shreeniketfatangare668]

ANS1) 0

[@DrMathaholic]

Thank you for posting the answer. Happy studying

[@aniruddhguranna6920]

Multiply your weight by the moon's gravity relative to earth's, which is 0.165.

[@DrMathaholic]

Yup.. correct!! 😀

[@invincibleinvincible3215]

Thanks a lot sir 🙂🙂🙂 polor coordinate me mujhe kafi doubt the aapne sare clear kar diye.

[@DrMathaholic]

Great.
Very happy to hear that..

[@preekshitchandel3981]

thank you so much sir ,it helps me a lot

[@DrMathaholic]

Happy to hear that..
Welcome 😀

[@mihirpandey4037]

Really great

[@DrMathaholic]

Thanks 😊

[@sandweepdas7459]

1/6 sir

[@DrMathaholic]

Cool👏👏

[@sarveshmankar6855]

Sir please can you find the Volume of the last example??? Because while double integration we get cot(90) which is undefined.....

[@DrMathaholic]

The 6th example ????

[@sarveshmankar6855]

@@DrMathaholic Yes sir!

[@aaryachaumal]

Is changing to polar coordinates similar to substitution ie x=rcos,y=rsin

[@DrMathaholic]

Yes..

[@yadneshgujar8991]

Sir can u plz tell, How can we use polar coordinates integration in the elliptical region x^2/a^2 + y^2 / b^2 =1 , what should substitution of r and theta for it?

[@DrMathaholic]

For this, one should know the notion of Jacobian. That you will be studying in next week. After that u can solve this easily.

[@yadneshgujar8991]

@@DrMathaholic thank you sir

[@DrMathaholic]

@@yadneshgujar8991 welcome 😀

[@aryarohanrachamalla2730]

Thx sir pls do upload more videos
And also pls tell reference books other than thomas calculus

[@DrMathaholic]

Welcome!!
If you are looking for any concept on which I have not made any video then you can let me know..
I will make it :)

[@DrMathaholic]

There is book on calculus by Stewart.
Schaum series is also good..

[@aryarohanrachamalla2730]

Sir pls explain the beta gamma functions in integration

[@DrMathaholic]

@@aryarohanrachamalla2730 hi Arya,
Hope this link will help you.
czcams.com/video/nkCJgdFObGQ/video.html

[@mrudulasawaikar4985]

Sir, can you please tell how can we find the r, theta values for circles with shifted centre. Like suppose the circle is of radius 1 and the centre is at (1,1)

[@DrMathaholic]

In such scenario replace x by r cos(t) and y by r sin(t) so u will get polar equation.

[@DrMathaholic]

For ex. Circle with center (1,0) and radius 1 i.e. (x-1)^2+y^2=1 so after substitution as said above you will get r= 2 cos(t). So limit will be 0 to 2 cos(t)

[@DrMathaholic]

Now try for the question you asked

[@mrudulasawaikar4985]

Thank you Sir, I understood it.

[@DrMathaholic]

@@mrudulasawaikar4985 great..all d bst!!

[@pranjalarbal2557]

H.W 1)0

[@DrMathaholic]

Thanks Pranjal for posting the answer.

[@shreeniketfatangare668]

3:51 1/6

[@DrMathaholic]

Correcto 😀

[@sandweepdas7459]

Intigration y=2 to 4 x=0 to √(4y-y^2). Sir isme r aur theta ka limit kya hoga

[@DrMathaholic]

Squaring, we get x^2+y^2-4y=0 , x^2+(y-2)^2=4...region is in first quadrant...
So r goes from 0 to 4 sin(theta) and theta goes from 0 to pi/2

[@sandweepdas7459]

@@DrMathaholic But y=2 to 4 sir . So limit of theta may be differ .

[@DrMathaholic]

@@sandweepdas7459 oh yes..my bad...
Limits of R will be from
2cosec(theta) to 4sin(theta)...limits of theta will be from pi/4 to pi/2...

[@boo4738]

Sir, thank you soooooooo much

[@DrMathaholic]

Welcome 😊

[@sagarmali4179]

Sir in last example , I think the limits for theta is wrong at 17:58. At first we have taken angle in triangle as theta and set the limits as between 60 and 90 . But after that we changed it and taken the angle in triangle as 90 - theta . So I think sir limits should also change. You applied the limits for theta as previous theta. Please check once and tell me if I am going wrong somewhere.

[@DrMathaholic]

I will check n get back to u Sagar..

[@DrMathaholic]

Its correct Sagar. We took (90- theta) while finding r.

[@DrMathaholic]

If (90-theta) confuses you, then do in this way:: y=root(3) implies r sin(theta)= root(3) implies r= cosec( theta)*root(3).

[@sagarmali4179]

@@DrMathaholic Got it sir. Thankss.

[@DrMathaholic]

@@sagarmali4179 good . Welcome.

[@pranjalarbal2557]

factor of magnification is 1/6

[@DrMathaholic]

Correct Pranjal!! Thanks for posting the answer 😀

[@aryarohanrachamalla2730]

Sir pls tell me how to solve 15th question in thomas calucus book pg 906

[@DrMathaholic]

Which edition?

[@aryarohanrachamalla2730]

@@DrMathaholic 14th edition sir

[@helloworld-hv9oy]

Theta is the angle made by radial lines?

[@DrMathaholic]

Theta is along x axis counterclockwise direction

[@helloworld-hv9oy]

@@DrMathaholic Actually i meant formal definition of theta 😅

[@DrMathaholic]

@@helloworld-hv9oy yes..

[@helloworld-hv9oy]

@@DrMathaholic Thank you !

[@DrMathaholic]

@@helloworld-hv9oy welcome

[@rosminjoseph3661]

1/6

[@DrMathaholic]

Thank you for posting the answer ☺️

[@kartikmandhan6990]

Answer to H.W
1. theta 0->π/4, r: 0->sec(theta)
2. theta: 0->3π/2, r:1->2

[@DrMathaholic]

Wlc back Kartik.. Thanks for posting the answer.

[@rakshithgowdahc9250]

3:45 1/6

[@DrMathaholic]

👏👏