Find the volume:
y=x^2 + 4, y=2x^2

Question

Find the volume: 
y=x^2 + 4, y=2x^2

anonymous · Answer

On what interval? The volume is infinite otherwise.

isabel☺ · Answer

no given

anonymous · Answer

The x^2+4 is important. Either you updated it or I didn't see it. 

It's important because we want to find out where the graphs intersect to know our limits of integration. 

Start by setting them equal, then solve for x to find the points of intersection. 

x^2+4=2x^2

Solve this for x and you find that they intersect at x = 2 and x = -2, So we integrate from 2 to -2

Let F(x)=x^2+4 and G(x)=2x^2

In this case F(x) is our outer radius and G(x) is our inner radius. 

Use the ring method to do this. Evaluate the integral:

$$\pi*\int\limits_{-2}^{2}(F(x)^2-G(x)^2)dx$$

and that will give you the volume. 

Look in your textbook for how the washer method for finding the volume of a solid of revolution works. If anything is unclear, ask something specific.

isabel☺ · Answer

does the graph looks like this? 
i really can't find the volume

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