Find out the surface area of the solid, Mathematics

Assignment Help:

Find out the surface area of the solid acquired by rotating y = √ (9-x2), - 2 < x < 2 about the x-axis.

Solution

The formula that we'll be using here is,

S = ∫ 2Πyds         

As we are rotating about the x-axis and we will make use of the first ds in this case since our function is in the correct form for this reason ds and we won't gain anything by solving it for x. Let us first get the derivative and the root taken care of.

Dy/dx = ½ (9-x2)- ½ (-2x)

= - x / (9-x2)½

√(1+ (dy/dx)2)

= √(1+ x2 / (9-x2))

= √(9 / 9-x2)

= 3/ √(9-x2)

Here's the integral for the surface area,

S = ∫2-2 2Πy (3/ √(9-x2)) dx

Though there is a problem. The meaning of dx here is that we shouldn't have any y's in the integral. Thus, before evaluating the integral we'll require to substitute in for y as well. After that the surface area is,

743_Find out the Surface Area of the solid.png


Related Discussions:- Find out the surface area of the solid

Hydrostatic pressure and force - applications of integrals, Hydrostatic Pre...

Hydrostatic Pressure and Force - Applications of integrals In this part we are going to submerge a vertical plate in water and we wish to know the force that is exerted on t

Multistage sampling, Multistage sampling Multistage sampling is similar...

Multistage sampling Multistage sampling is similar to stratified sampling except division is done on geographical/location basis, for illustration a country can be divided into

More optimization problems, More Optimization Problems Example   A w...

More Optimization Problems Example   A window is being built in which the bottom is rectangle and the top is a semicircle. If there framing materials is 12 meters what have

Computation of covariance - ungrouped data, Computation of Covariance ...

Computation of Covariance Ungrouped Data          For a population consisting of paired ungrouped data points {X, Y} where,

Show that aq= 1/2 perimeter of triangle abc, A circle touches the side BC o...

A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R. Show that AQ= 1/2 (perimeter of triangle ABC) Ans:    Since the length o

Show that the function f is one-one but not onto, Consider the function f: ...

Consider the function f: N → N, where N is the set of natural numbers, defined by f(n) = n 2 +n+1. Show that the function f is one-one but not onto. Ans: To prove that f is one

Solve factors for given equations, 1/a+b+x  =1/a+1/b+1/x    a+b ≠ 0 ...

1/a+b+x  =1/a+1/b+1/x    a+b ≠ 0 Ans: 1/a+b+x  =1/a+1/b+1/x => 1/a+b+x -1/x = +1/a +1/b ⇒  x - ( a + b + x )/ x ( a + b + x )   = + a + b/ ab ⇒

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