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

Rectilinear figures, what are rctilinear figures ? types of rectilinear fig...

what are rctilinear figures ? types of rectilinear figures and their propertiees.

Pythagorean theorem, when one side of a triangle is 15cm and the bottom of ...

when one side of a triangle is 15cm and the bottom of the triangle is 12cm what would x be rounded to the nearest tenth?

Applications of derivatives, Applications of derivatives : At last, let's ...

Applications of derivatives : At last, let's not forget about our applications of derivatives. Example    Assume that the amount of air in a balloon at any time t is specified

Total accumulation of the amount deposited in saving account, A bank pays o...

A bank pays on its savings an interest rate of 6% per year but compounds interest monthly (i.e., estimates the interest each month and adds it to the balance).  You plan to deposit

Frequency polygon, how to compute the frequncy polygon of the scores?

how to compute the frequncy polygon of the scores?

Arc length for parametric equations, Arc Length for Parametric Equations ...

Arc Length for Parametric Equations L = ∫ β α √ ((dx/dt) 2 + (dy/dt) 2 ) dt Note: that we could have utilized the second formula for ds above is we had supposed inste

Fractions, what the answer to 1/4+1/3=3/12=?

what the answer to 1/4+1/3=3/12=?

Triangles, ABCD is a parallelogram which AB and CD are divides by P and Q. ...

ABCD is a parallelogram which AB and CD are divides by P and Q. Such that AP:PB=3:2 and CQ:QD=4:1. If PQ and AC are meet at R, show that AR=3/7AC.

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