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

Find the area of shaded region, Find the area of shaded region, if the side...

Find the area of shaded region, if the side of square is 28cm and radius of the sector is ½ the length of side of square.

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

Circles, Circles In this section we are going to take a rapid look at ...

Circles In this section we are going to take a rapid look at circles.  Though, prior to we do that we have to give a quick formula that expectantly you'll recall seeing at som

Find out the determinant, Find out the determinant: Find out the deter...

Find out the determinant: Find out the determinant of the following 3 x 3 matrix, expanding about row 1. Solution:

Integers, Explain with the help of number line (-6)+(+5)

Explain with the help of number line (-6)+(+5)

Linear programming , A paper mill produces two grades of paper viz., X and ...

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

Calculate the monthly payment amount of the loan, Consider a student loan o...

Consider a student loan of $12,500 at a fixed APR of 12% for 25 years, 1. What is the monthly payment amount? 2. What is the total payment over the term of the loan? 3. OF

Michael has 16 cds how many cds does kathleen have, Michael has 16 CDs. Th...

Michael has 16 CDs. This is four more than twice the amount that Kathleen has. How many CDs does Kathleen have? Let x = the number of CDs Kathleen has. Four more than twice th

Sphere and cone, How tall does a cone with diameter of 10 inches have to be...

How tall does a cone with diameter of 10 inches have to be to fit exactly half of a sphere with a diameter of 10 inches inside it?

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