You are here:

Calculus/Re: Calculs

Advertisement

Expert: Alon Mandes - 7/30/2009


Question
QUESTION: Hi prof i have one more question please chk this out tooo.

Find the volume of the solid obtained by rotating the region bounded by the curves
         y = 0, y = sinx, 0 ≤  x ≤  π; about the line y = -2.

ANSWER: In this section we have the formula of the volume is :
π
∫π[Ro²-Ri²] dx . Where Ro is the outer Radius, & Ri is the inner Raduis :
0
Ri=0-(-2)=2
Ro=sinx-(-2)=2+sinx
Therefore :
π
∫π[(2+sinx)²-2²] dx =
0
π
∫π[(4+2sinx+sin²x-4] dx =
0
  π          π
2π∫sinx dx + π∫sin²x dx =
0          0

I will leave both integrals for you as an exercise.

Alon.




---------- FOLLOW-UP ----------

QUESTION: i solved the other steps and i got the answer

5pi.

is it ok

please help me out if i m wrong the please send me the other steps too.

Answer
π          π
2π∫sinx dx + π∫sin²x dx =
0          0

2π[-cosx] + π½[x-cosxsinx] =
{0->π}        {0->π}

2π[-cosπ-1] + ½π[π-cosπsinπ+0cos0sin0]=

=½π²

Alon.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

©2012 About.com, a part of The New York Times Company. All rights reserved.