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

Determine the line parallel or perpendicular, Determine if the line that pa...

Determine if the line that passes through the points ( -2, -10) and (6, -1) is parallel, perpendicular or neither to the line specified  by 7 y - 9 x = 15 . Solution Togive

Differential equation - maple, 1. Consider the following differential equat...

1. Consider the following differential equation with initial conditions: t 2 x'' + 5 t x' + 3 x = 0, x(1) = 3, x'(1) = -13. Assume there is a solution of the form: x (t) = t

Estimate how much should every friend pay, A group of ?ve friends gone out ...

A group of ?ve friends gone out to lunch. The total bill for the lunch was $53.75. Their meals all cost about the similar, so they needed to split the bill evenly. Without consider

Solid Mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

Capture a curvature in the relationship - quadratic model, 1. Consider the ...

1. Consider the model Y t = β 0 + β 1 X t + ε t , where t = 1,..., n.  If the errors ε t are not correlated, then the OLS estimates of  β 0   and β

Stratified sampling, Stratified sampling In stratified sampling case t...

Stratified sampling In stratified sampling case the population is divided into groups in such a way that units in each group are as same as possible in a process called strati

Determine the price paid for a land, A parcel of land, value $250,000 is so...

A parcel of land, value $250,000 is sold to an investor who signs a contract agreeing to pay a deposit of $25,000 followed by equal quarterly payments for as long as necessary, wit

Mr, Probability of A is 85% Probability of B is 45% Probability A and B 56%...

Probability of A is 85% Probability of B is 45% Probability A and B 56% What is the probability of not either A or B?

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