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

Integration techniques, Integration Techniques In this section we are ...

Integration Techniques In this section we are going to be looking at several integration techniques and methods. There are a fair number of integration techniques and some wil

Complex roots - second order differential equations, We will be looking at ...

We will be looking at solutions to the differential equation, in this section ay′′ + by′ + cy = 0 Wherein roots of the characteristic equation, ar 2 + br + c = 0 Those

Hours, jeff left hartford at 2:15 pm and arrived in boston at 4:45 pm how l...

jeff left hartford at 2:15 pm and arrived in boston at 4:45 pm how long did the drive take him?

Determine the largest possible domain and inverse function, Consider the fu...

Consider the function f(x) =1/2 (2 x +2 -x ) which has the graph (a) Explain why f has no inverse function. You should include an example to support your explanation

Example of substitution method of linear equations, Describe some Example o...

Describe some Example of substitution method of Linear Equations with solution.

Fractions, how can I compare fractions with unlike denominators?

how can I compare fractions with unlike denominators?

Math, what is the changen intemperature bewtween the highest and the lowest...

what is the changen intemperature bewtween the highest and the lowest temperture high-40c low-0c

Do yall, do yall help kids in 6th grade

do yall help kids in 6th grade

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