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MAC5494
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Question
I'm really having issues grasping the Volumes of Solids of revolution. I could use some help solving this question, it isn't very hard.
1. Let R be the region bounded by y = x2 and y = x + 2. Find:
a) the area of R
b) the volume of the solid if R is rotated about the x-axis
c) the volume of the solid if R is rotated about the the line x = 4
Basically this is what I've gotten.
a)
Area = ∫((x+2)-(x2))dx
= (x2/2 + 2x) - (x3/3), evaluated over the interval (-1,2)
= 4.5
b) this is what I did but I don't know if it is right
∏∫((x+2)2 - (x2))dx
= ∏∫((x2+4x+4) - x4) dx
= ∏(x5/5 - x3/3 -2x2 -4x) evaluated from (-1,2)
= 72∏/5
c) I'm not sure how to start this one.
I'm really having issues grasping the Volumes of Solids of revolution. I could use some help solving this question, it isn't very hard.
1. Let R be the region bounded by y = x2 and y = x + 2. Find:
a) the area of R
b) the volume of the solid if R is rotated about the x-axis
c) the volume of the solid if R is rotated about the the line x = 4
Homework Equations
The Attempt at a Solution
Basically this is what I've gotten.
a)
Area = ∫((x+2)-(x2))dx
= (x2/2 + 2x) - (x3/3), evaluated over the interval (-1,2)
= 4.5
b) this is what I did but I don't know if it is right
∏∫((x+2)2 - (x2))dx
= ∏∫((x2+4x+4) - x4) dx
= ∏(x5/5 - x3/3 -2x2 -4x) evaluated from (-1,2)
= 72∏/5
c) I'm not sure how to start this one.