Find the volume of the solid generated when the region under the curve y = 1/(x^2 + 3x + 2) from x = 0 to x = 1 is revolved about the given axis. Make certain to include sketches and justifications for each solid.

a. x-axis
b. y-axis

Question

Find the volume of the solid generated when the region under the curve y = 1/(x^2 + 3x + 2) from x = 0 to x = 1 is revolved about the given axis. Make certain to include sketches and justifications for each solid.

a. x-axis
b. y-axis

amistre64 · Answer

youll most likely have to complete the square on the bottom and see if this changes into a 1/(u^2+1) format

amistre64 · Answer

or do alot of partial decmomps

amistre64 · Answer

decompositions

anonymous · Answer

(x+1)(x+2)

amistre64 · Answer

hmmm, if you wanna go that route, partial decomp then

amistre64 · Answer

either way, the radius is squared to find the area if a circle ....  might wanna go ahead and plug a ^2 on those

anonymous · Answer

doesn't matter, that's the same thing

amistre64 · Answer

$$\frac{1}{(x-a)^2(x-b)^2}=\frac{A}{x-a}+\frac{Bx+C}{(x-a)^2}+\frac{D}{x-b}+\frac{Ex+F}{(x-b)^2}$$

anonymous · Answer

i can integrate but my problem is, i can't make an equation

amistre64 · Answer

when x=a

$$1=\frac{D}{a-b}+\frac{Ea+F}{(a-b)^2}$$

etc... gives you a system of equations to play with in the end

amistre64 · Answer

you can make an equation?

anonymous · Answer

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