# Math Help - Help with a problem in maple

1. ## Help with a problem in maple

I need help with following maple problem. All I need help with right now is finding the a and b in part a. If I have any problems later, I may be back for more help, but right now I just need help finding a and b. Anyway here is the problem:

Let S be the solid obtained by revolving the region bounded between
1
u(x) = - x + 2
2

and
1 2
v(x) = 7 - - x + sin(x)
5
; around the horizontal line
y = -2
.

a. (4 points) Define functions u and v of x using the arrow notation. Find the x-values of the two points of intersection and give them the names a and b. Hint: a will be negative and b will be positive.
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>

b. (3 points) Plot your functions u and v together with a representative vertical rectangle. Include the axis of rotation (the line
y = -2
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c. (2 points) Use animatesor (using the option
method = washers
) and plotsor to plot the solid of revolution. Use the option
scaling = constrained
in both commands.
>
>

d. (3 points) Use integration to find the volume of the solid S correct to ten significant digits. (Your answer should be between 1000 and 1500 cubic units.)
>
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I am not sure how to get a and b in part a of the above problem. Do I plug in -2 into the equations and that will give me my a and b? Or do I need to solve something in maple to figure out what they are? Anyone know what I am supposed to do? I'm kind of lost. Thanks in advance to anyone who can help.

2. I am not sure why my functions didn't show up correctly in my post, but they should be v(x) = 7-(1/5)*x^2+sin(x) and u(x) = (1/2)*x+2. Sorry about that.

3. I really dont understant what you want, but I have some codes that can help you.

Code:
u:=x->x^2/2+1; #define the function

img.top {vertical-align:15%;}

$u$
Au:={solve(u(x)=1,x)}; #solve

img.top {vertical-align:15%;}

$u(x)=1$ with respect to

img.top {vertical-align:15%;}

$x$
Bu:={solve(u(x)=2,x)}; #solve

img.top {vertical-align:15%;}

$u(x)=2$ with respect to

img.top {vertical-align:15%;}

$x$
plot(u(x),x=Bu[2]..Bu[1]); #plot u by considering

img.top {vertical-align:15%;}

$-\sqrt{2}\leq x \leq\sqrt{2}$

4. I am wanting to know what the values of a and b values are for the functions v(x) = 7-(1/5)*x^2+sin(x) and u(x) = (1/2)*x+2 around the horizontal line y=-2. I have already defined v(x) and u(x) using arrow notation in a previous step and now just want the values for a and b, but can't figure out how to get them.Oh, and this problem is from a section called Volume: The Disk Method in my textbook, if that helps any. Usually a and b are just given to me, but in this problem they aren't and I can't figure out how to get them. Should I just plug -2 into the statements or should I do an fsolve or something to find the values of a and b. Thanks in advance to anyone who can help.