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I have been having trouble with this kind of problem lately and I need to know if what I have done here is right (calculator problem but I have not evaluated anything yet):

Let R be the region bounded by the y-axis and the graphs of

[tex]y=\frac{x^3}{1+x^2}[/tex] and

[tex]y=4-2x[/tex]

a) Find the area of R

b) Find the volume of the solid generated when R is revolved about the x-axis

c)The region R is the base of a solid. For this solid, each cross section parallel to the x-axis is a square. Find the volume of this solid.

a)

a=point of intersection of the two graphs

[tex]\int_0^a(4-2x-\frac{x^3}{1+x^2})dx[/tex]

b)

[tex]{\pi}\int_0^a(4-2x)^2-(\frac{x^3}{1+x^2})^2dx[/tex]

c)

[tex]\pi \int_0^a(4-2x-\frac{x^3}{1+x^2})^2dx[/tex]

Let R be the region bounded by the y-axis and the graphs of

[tex]y=\frac{x^3}{1+x^2}[/tex] and

[tex]y=4-2x[/tex]

a) Find the area of R

b) Find the volume of the solid generated when R is revolved about the x-axis

c)The region R is the base of a solid. For this solid, each cross section parallel to the x-axis is a square. Find the volume of this solid.

a)

a=point of intersection of the two graphs

[tex]\int_0^a(4-2x-\frac{x^3}{1+x^2})dx[/tex]

b)

[tex]{\pi}\int_0^a(4-2x)^2-(\frac{x^3}{1+x^2})^2dx[/tex]

c)

[tex]\pi \int_0^a(4-2x-\frac{x^3}{1+x^2})^2dx[/tex]

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