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.
10p=100
if A be the area of a right triangle and b be one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2Ab/rootb^4+4A^2
use the expansion of (1-x)^7 to find the value of 1.998^7 correct to five significant figures
Kyra receives a 5% commission on every car she sells. She received a $1,325 commission on the last car she sold. What was the cost of the car? Use the proportion part/whole =
solve the inequality (2^x+1)(3^x+1)(4^x+1)
A man sold an item for Rs 6,750 at a loss 25%. What will be the selling price of same item if he sells it at a profit of 15%?
A medical survey was conducted in order to establish the proportion of the population which was infected along with cancer. The results indicated that 40 percent of the population
Integrate following. ∫ -2 2 4x 4 - x 2 + 1dx Solution In this case the integrand is even & the interval is accurate so, ∫ -2 2 4x 4 - x 2 + 1dx = 2∫ o
darien agrees to sponsor her sister $8 plus $1 for every mile she walks.Write an expression to show her total money
how can i find the online students ?
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