Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
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 dθ
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.
Spurious Correlations - in several rare situations when plotting the data for x and y we may have a group indicating either positive correlation or negative (-ve) correlation
what is 24 diveded by 3
Decision making under uncertainty Various methods are used to make decision in circumstances whereas only the pay offs are identified and the likelihood of every state of natur
Left-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x Note that the change in notation is extremely m
Example of Integration by Parts - Integration techniques Some problems could need us to do integration by parts many times and there is a short hand technique that will permit
#questionQn 1- An analysis of monthly wages of workers of two organizations Alia LLC and Asila LLC yielded the following results. Alia LLC Asila LLC Average monthly wages 60
g/6-2+(9/9)
who discovered unitary meathod
In this section we will be searching how to utilize Laplace transforms to solve differential equations. There are various types of transforms out there into the world. Laplace tran
Give an Equations with the variable on both sides ? Many equations that you encounter will have variables on both sides. Some of these equations will even contain grouping sy
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!
whatsapp: +91-977-207-8620
Phone: +91-977-207-8620
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd