Surface area with polar coordinates, Mathematics

Assignment Help:

Surface Area with Polar Coordinates

We will be searching for at surface area in polar coordinates in this part.  Note though that all we're going to do is illustrate the formulas for the surface area as most of these integrals tend to be quite difficult.

 We want to locate the surface area of the region found through rotating,

r = f (θ)

α < θ < β

about the x or y-axis.

Like we did in the tangent and arc length sections we will write the curve in terms of a set of parametric equations.

x= r cosθ

= f (θ) cos θ

y = r sin θ

= f (θ) sin θ

If we now make use of the parametric formula for finding the surface area we'll obtain,

S = ∫ 2Πy ds                             rotation about x-axis

S = ∫ 2Πx ds                             rotation about y-axis

Where

ds = √r2 + (dr/dθ)2

r = f (θ) , α < θ < β

Note: since we will pick up a  dθ  from the ds we'll require to substitute one of the parametric equations in for x or y depending upon the axis of rotation.  This will frequently mean that the integrals will be rather unpleasant.


Related Discussions:- Surface area with polar coordinates

Consumer behaviour, what is consumer behaviour according to accounting

what is consumer behaviour according to accounting

Ecercises, ne nje tabak letre me permasa 100cm dhe 55cm nje nxenes duhet te...

ne nje tabak letre me permasa 100cm dhe 55cm nje nxenes duhet te ndertoje nje kuboide me permasa 20cm,25cm,40cm. a mund ta realizoje kete, ne qofte se per prerjet dhe ngjitjet humb

What is common triangles, Q. What is Common Triangles? Ans. Some t...

Q. What is Common Triangles? Ans. Some triangles appear more commonly than others. You will come across two triangles repeatedly as you learn more about trigonometry. T

Quadratic equations by completing the square method, Can we solve the Quadr...

Can we solve the Quadratic Equations by completing the square method? if yes explain it.

How long will it take to dispense 330 gallons, A large pipe dispenses 750 g...

A large pipe dispenses 750 gallons of water in 50 seconds. At this rate, how long will it take to dispense 330 gallons? Find out the number of gallons per second by dividing 75

Ways for 30 identical balls can be distributed among 4 boys, In how many w...

In how many ways 30 identical balls can be DISTRIBUTED among 4 boys?? Ans) Let they get a,b,c,d respectively. You requireto find the non negative integral results of a+b+c+d=3

What is the difference in the two low temperatures, The low temperature in ...

The low temperature in Anchorage, Alaska present was -4°F. The low temperature in Los Angeles, California was 63°F. What is the difference in the two low temperatures? Visualiz

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd