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 out a series solution for differential equation, Find out a series sol...

Find out a series solution for the following differential equation about x 0 = 0 y′′ + y = 0.   Solution Note that in this case p(x)=1 and therefore every point is an or

????? ???????, ???? ????? ??????? ?? ????? ??? ?? ????? ??????? ??????

???? ????? ??????? ?? ????? ??? ?? ????? ??????? ??????

Properties of logarithms, Properties of Logarithms 1. log a x...

Properties of Logarithms 1. log a xy = log a x + log a y 2.  = log a x - log a y 3. log a x n   = n log

Polynomials, for what value of k,the following system of equations have inf...

for what value of k,the following system of equations have infinite solutions?kx + 5y -(k-5)=0;20x +ky - k=0

Cylindrical coordinate system, how to describe the locus of the equation x^...

how to describe the locus of the equation x^2+6xy+y^2+z^2=1 in cylindrical polar coordinates?

Find the cost price of the toy, A dealer sells a toy for Rs.24 and gains as...

A dealer sells a toy for Rs.24 and gains as much percent as the cost price of the toy. Find the cost price of the toy. Ans:    Let the C.P be x ∴Gain = x % ⇒ Gain = x

What is the net surface area to be painted, You are painting the surface of...

You are painting the surface of a silo that has a diameter of 16 ft and height of 50 ft. What is the net surface area to be painted? Consider the top of the silo is  1/2 a sphere

Estimate the grade resistance, The grade resistance is F=W sin θ, where θ i...

The grade resistance is F=W sin θ, where θ is the grade and W is the weight of the automobile.  What is the grade resistance of a 2500 pound car traveling on a 2.6 degree uphill gr

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 %

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