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.
what is 10+10
a conical vessel of radius 6cm and height 8cm is completely filled with water.a sphere is lowered into the water and its size is such that when it touches the size it is immersed.w
1,5,14,30,55 find the next three numbers and the rule
On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if q(x)=ax^(2)+bx+c, find a,b and c.
1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is dierent
Any 15 foot ladder is resting against the wall. The bottom is at first 10 feet away from the wall & is being pushed in the direction of the wall at a rate of 1 ft/sec. How rapid is
Brewery has 12 oz bottle filling machines. Amount poured by machine is normal distribution mean 12.39 oz SD 0.04 oz. Company is interested in in reducing the amount of extra beer
Q. Define Number Line? Ans. A number line is a nice way to visualize and examine the ordering of the positive and negative numbers. Every positive and negative number that
Mean Value Theorem : Suppose f (x) is a function which satisfies both of the following. 1. f ( x )is continuous on the closed interval [a,b]. 2. f ( x ) is differentiable on
Right- and left-handed limits : Next, let's see precise definitions for the right- & left-handed limits. Definition For the right-hand limit we say that, if for eve
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