Purchase Solution

disc method

Not what you're looking for?

Ask Custom Question

Find the volume of the solid that is generated by rotating around the indicated axis the plane region bounded by the fiven curves.

1) y=√x,y=0,x=4; The x-axis
2) y= 1/x, y=0, x=0.1,x=1; the x-axis

3)Find the volume of the ellipsoid generated by rotating around the x-axis the region bounded by the ellipse with equation.
(x/a)^2 + (y/b)^2 =1

4) (a) Find the volume of the unbounded solid generated by rotating the unbounded region around the x-axis. This is the region between the graph of y=e^-x and the x-axis for x >1. (Compute the volume from x=1 to x=b, where b>1. Then find the limit of this volume as b->+∞).
(b) What happens if y= 1/√x instead?

Purchase this Solution
Solution Summary

The volume of solids and ellipsoid for an unbounded solid are determined.

Solution Preview

(1) By the disc method we get

pi. int._{0 to 4} (sqrt(x))^2 dx = 8 .pi

Using cylindrical shells we get

2.pi int_{0 to 2} y (4 - y^2) dy = 2.pi (8 - 4) = 8.pi

(2) the ...

Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

View More Free Quizzes
Related BrainMass Solutions

  • Cost Equation/Account Classification Method

    129976 Cost Equation/Account Classification Method A. Develop the cost equation for Mr. Smith's store, using the account classification method, assuming that the cost object is the individual compact disc. b. Mr.

  • Integration : Finding Volume of a Disc

    51278 Integration : Finding Volume of a Disc Find the volume of y = 1/sqrt(1+x^2) bounded by y=0, x=-1, x=1 I'm using the disc method with a dx function: V = pi integral( [R(x)]^2 ) dx Therefore, I have V = pi integral( [1/sqrt(1+x^2)] ^2

  • c++ recursion

    Code for hanoi tower problem is written using Recursion method.

  • Advanced dynamics of a spinning disk

    Direction of the angular velocity (angle ): By the direction formula from parallelogram method, i.e. i.e. i.e. tan  = -0.00837 i.e.  = tan-1 (-0.00837) i.e.  = 0.479530 i.e. 28' 57.18" (28 min 52.17 sec.)

  • Potential Equation on a Disc : Dirichlet

    The most usual method to do that is the Fourier method, that means using separation of variables.

  • Incremental Analysis and Special Orders

    This solution shows step-by-step calculations to determine if the Henson Company should accept the special offer using the incremental analysis method. It also states the assumptions for the analysis.

  • Leadership Development and DiSC Assessments

    In the past 40 years, some 35+ million people have taken the DiSC test in 30-odd different languages. Reference: Resources Unlimited (2015). DiSC Profiles and Training. Retrieved from: http://www.disctests.com/what-is-disc?

  • Average Angular Acceleration

    70696 Average Angular Acceleration Compact Disc. A compact disc (CD) stores music in a coded pattern of tiny pits 10^(- 7) m deep.

  • Discs

    (b) Distinguish between the annulus fibrosus and nucleus plposus regions of a disc. (c) Which provides durability and strength? (d) Which provides resilience? (e) Which part is involved in a "slipped" disc? a.

  • Disc in a Magnetic Field Conductivity

    67420 Disc in a Magnetic Field Conductivity Given an aluminum disc of radius R, thickness d, conductivity , and mass density spins on its axis with initial velocity .

View More Related Solutions