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

The Theory of Set, Set M= {m''s/m is a number from 5 to 10}

Set M= {m''s/m is a number from 5 to 10}

Estimate the last month sales increased through only 1/2%, Sales increased ...

Sales increased through only 1/2% last month. If the sales from the previous month were $152,850, what were last month's sales? Multiply through the decimal equivalent of 1/2 %

Elementary row operations, Anne, Betty and Carol went to their local produc...

Anne, Betty and Carol went to their local produce store to buy some fruit. Anne bought one pound of apples and two pounds of bananas and paid $2.11. Betty bought two pounds of appl

Ratios, in a veggie mix the ratio of cups of carrots to cups of broccolie i...

in a veggie mix the ratio of cups of carrots to cups of broccolie is 4 to 5 if you made this party mix larger how many cups of carrots would be needed to mix with fo cups of brocco

Quadratic equation, can anyone explain me the concept of quadratic equation...

can anyone explain me the concept of quadratic equation?

Objective functions, For schedule consistency, you decide to require each o...

For schedule consistency, you decide to require each officer to report for their eight-hour shift at 12 AM, 4 AM, 8 AM, 12 PM, 4 PM, or 8 PM. As the Director of Public Safety, you

Subset [tabular method], 1.A=the set of whole numbers less tan 4 ? 2.B=the ...

1.A=the set of whole numbers less tan 4 ? 2.B=the set of prime numbers less than 19 ? 3.C=the set of first three days of week?

Determine the area of the shaded region, The diagram below shows the cross ...

The diagram below shows the cross section of a pipe  1/2  inch thick that has an inside diameter of 3 inches. Determine the area of the shaded region in terms of π. a. 8.75π i

All subjects, I need help. Is there anyone there to help me?

I need help. Is there anyone there to help me?

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