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

Whats this, how do you determine if a graph has direct variation

how do you determine if a graph has direct variation

Method of disks or the method of rings, Method of disks or the method of ri...

Method of disks or the method of rings One of the simple methods for getting the cross-sectional area is to cut the object perpendicular to the axis of rotation.  Carrying out

Standard trig equation, "Standard" trig equation: Now we need to move into...

"Standard" trig equation: Now we need to move into a distinct type of trig equation. All of the trig equations solved to this point were, in some way, more or less the "standard"

Calculate the cost make use of trigonometric functions, In this task you ar...

In this task you are required to make use of trigonometric functions, research and use the Monte Carlo method of integration to determine areas under curves and perform calculation

We know this equation a°=1.prove this?, we know that log1 to any base =0 ta...

we know that log1 to any base =0 take antilog threfore a 0 =1

He would such as to leave 20% tip how much should he leave, Mr. Pelicas too...

Mr. Pelicas took his family out to dinner. The bill was $65.00. He would such as to leave a 20% tip. How much should he leave? Find 20% by multiplying $65 through the decimal e

Fundamental theorem of integral facts , Fundamental Theorem of Calculus, Pa...

Fundamental Theorem of Calculus, Part II  Assume f(x) is a continuous function on [a,b] and also assume that F(x) is any anti- derivative for f(x). Hence, a ∫ b f(x) dx =

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