Find the volume of the solid with base bounded by y=x²-2 and y=4 and square cross-sections

[bigskilly]

Find the volume of the solid formed with a base bounded by y = (x^2)-2 and y=4 filled with squares that are perpendicualr to the x-axis.

 

[leyade]

...i think you can find that area using simpson's rule , you can thus proceed to find the volume using the maximum height...yeah i think that should work...

 

[Giuseppe]

It's really not necessary to use Simpson's Rule. Find an volume by cross-section. In order to do that, you need to develop an equation for the area, in this case a square. By the equations you gave, the length of one side of the square would be $$4-[(x^2)-2]$$. Since the cross-sections are perpendicular to the x axis. You can leave the function as is since it is already in terms of x. So the formula for volume by cross-sections is

$$\int^a_b A(x)\delta x$$

so after finding your a and b, (set the equations equal to each other)

you get the $$\int^2_{-2} {4-[x^2-2)]}^2 \delta x=16$$