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

Which of the following could not be the translation, If the expression 9y -...

If the expression 9y - 5 represents a certain number, which of the following could NOT be the translation? a. five less than nine times y b. five less than the sum of 9 and y c

upper and lower limits, A critical dimension of the service quality of a c...

A critical dimension of the service quality of a call center is the wait time of a caller to get to a sales representative. Periodically, random samples of 6 customer calls are mea

Geometric mean-geometric progression, Geometric mean - It is a measure ...

Geometric mean - It is a measure of central tendency normally utilized to measure industrial increases rates. - It is explained as the nth root of the product of 'n' observa

Problem solving, Let E; F be 2 points in the plane, EF has length 1, and le...

Let E; F be 2 points in the plane, EF has length 1, and let N be a continuous curve from E to F. A chord of N is a straight line joining 2 points on N. Prove if 0 and N has no cho

Why x and y are simplifying expressions, Why x and y are Simplifying Expres...

Why x and y are Simplifying Expressions? You're doing algebra now, and you know you're going to see x's and y's. But before we work with x's and y's, we'll explore why we use t

What is the least number of students needed in a class, What is the least n...

What is the least number of students needed in a class to be sure that at least 6 will receive similar grade if there are five probable grades A, B,C, D and F?  Ans: Let us re

Calculus, what is a domain of a function?

what is a domain of a function?

Determine radicals in exponent form, Evaluate following.               ...

Evaluate following.                √16 and Solution To evaluate these first we will convert them to exponent form and then evaluate that since we already know how to

What is her weekly paycheck assuming there are deductions, Kyra's weekly wa...

Kyra's weekly wages are $895. A Social Security tax of 7.51% and a State Disability Insurance of 1.2% are taken out of her wages. What is her weekly paycheck, assuming there are no

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