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

Solve-|x2-5x+4/x2-4|

x^2-5x+4 can written in roots as (x-1)*(x-4) x^2-4 can be written interms of (x-2)(x+2).so [(x-1)(x-4)/(x-2)(x+2)]

Inverse functions, We have seen that if y is a function of x, then fo...

We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f

lmc, what is the concept of lm

what is the concept of lmc

Angles, how to measure missing angle of an adjacent angle

how to measure missing angle of an adjacent angle

Example of implicit differentiation, Example of Implicit differentiation ...

Example of Implicit differentiation So, now it's time to do our first problem where implicit differentiation is required, unlike the first example where we could actually avoid

Lesson 3.5 skills practice, Noah is renewing a magazine subscription. one p...

Noah is renewing a magazine subscription. one package offers to renew the magazine for 3 years for 26$. A second package offers to renew the magazine for 5 years for $38

Variance-measure of central tendency, Variance Square of the standard...

Variance Square of the standard deviation is termed as variance. The semi inter-quartile range - It is a measure of dispersion which includes the use of quartile. A q

Differential equation, Cos(x+y)+sin(x+y)=dy/dx(solve this differential equa...

Cos(x+y)+sin(x+y)=dy/dx(solve this differential equation)

Law of Sine and Cosine Word Problems, A poll tilts towards the sun at an 8 ...

A poll tilts towards the sun at an 8 o angle from the vertical at it casta 22-ft shadow. The angle of elevation from the shadow to the top of the pole is 43 o . How tall is th

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