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

Mr F.D, how you divide 100 by 10 and then x by 10

how you divide 100 by 10 and then x by 10

Explain equation, Equation s(in Tth second)=u+at-a/2 seems to be dimensiona...

Equation s(in Tth second)=u+at-a/2 seems to be dimensionally incorrect.why?

Evaluate integrals (1 - (1 /w) cos (w - ln w) dw, Evaluate following integr...

Evaluate following integrals.                       ( (1 - (1 /w) cos (w - ln w) dw Solution In this case we know how to integrate only a cosine therefore let's makes th

Math help, What fraction of the full price will you pay for 2 shirts? 3 4 ...

What fraction of the full price will you pay for 2 shirts? 3 4 11 2 $45.001 2 .

Can tan theeta be integrated?, Normal 0 false false false ...

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

Distance and Section Formulae, find the coordinates of points of tri-sectio...

find the coordinates of points of tri-section of the line joining the points (-3,0) and (6,6).

Trignometry, prove that sin A /cot A + cosec A = 2 + sinA / cot A - cosec A...

prove that sin A /cot A + cosec A = 2 + sinA / cot A - cosec A

Mathematical methods of economic analysis, I need answers for these 10 exam...

I need answers for these 10 exam questions: 1.Input-output (Leontief) model: main assumptions and construction. Definition of productivity. Necessary condition of productivity of i

What is the formula to calculate area of rectangle, Charlie needs to know t...

Charlie needs to know the area of his property, that measures 120 ft through 150 ft. Which formula will he use? The area of a rectangle is length × width.

Math, weather prediction on monsoon past data on project

weather prediction on monsoon past data on project

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