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

Shares and divend, a company of 10000 shares of rs 100 each declares a annu...

a company of 10000 shares of rs 100 each declares a annual dividend of 5 %.what is the total amount dividend paid by the company

Permutation and combination, The remainder when 5^99 is divided by 13 Ans) ...

The remainder when 5^99 is divided by 13 Ans) 8 is the remainder.

Functions, find the derived functions

find the derived functions

Area of a circle, How do you find the area of a circle given the diameter?

How do you find the area of a circle given the diameter?

Find out the area of the circle, 1. The number of accidents attended to by ...

1. The number of accidents attended to by 6 emergency ambulance stations during a 5 month period was: Station May June July Aug Sep      A        21     20     22    37    37

Elimination, Eliment t from following equations v=u+at s=ut+1/2at^2

Eliment t from following equations v=u+at s=ut+1/2at^2

?, x/15=50/20

x/15=50/20

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