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

I-phones in one year, Assume company A expects to enhance unit sales of i-p...

Assume company A expects to enhance unit sales of i-phone by 15% per year for the next 5 years. If you presently sell 3 million i-phones in one year, how many phones do you expect

Help, how do i know what operation to use in a fraction word problem

how do i know what operation to use in a fraction word problem

Dora, dora and her family are driving to visit relatives for the holidays t...

dora and her family are driving to visit relatives for the holidays they travel 174 miles in 3 hours if they travel at a constant speed how many miles do they travel in one hourest

Pattern, 1,5,14,30,55 find the next three numbers and the rule

1,5,14,30,55 find the next three numbers and the rule

Describe order of operations with example, Describe Order of Operations wit...

Describe Order of Operations with example? The order of operations is a set of rules that describe the order in which math operations are done. Try doing this math problem:

Binomial distribution, Binomial Distribution Consider a batch of N ligh...

Binomial Distribution Consider a batch of N light bulbs. Each bulb may be defective (S) or non-defective (F). The experiment involves selecting a light bulb and checking whethe

lmc, what is the concept of lm

what is the concept of lmc

Multiplication and division, you want to share 34 pencils among 6 friends ....

you want to share 34 pencils among 6 friends .How many would each friend get?

Define symmetric, Define symmetric, asymmetric and antisymmetric relations....

Define symmetric, asymmetric and antisymmetric relations.    Ans: Symmetric Relation A relation R illustrated on a set A is said to be a symmetric relation if for any x,

Estimate the area of this field in terms of x and y, Jonestown High School...

Jonestown High School has a soccer field whose dimensions can be expressed as 7y 2 and 3xy. What is the area of this field in terms of x and y? Since the area of the soccer ?e

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