## Fey 2 years ago Calculus: The region in the first quadrant bounded by the graphs of the equations y=(1/x), x=1, x=2, is revolved around the x-axis. Use the shell method to find the volume of the resulting solid.

1. Fey

I need help finding h(y),,,, (Height)

2. klimenkov

|dw:1360447641218:dw|

3. Fey

m,,, ok, I know the bounds are [1,2], the radius is y.... now, the height i want to say (1/y)-1????

4. klimenkov

$$V=\pi\int \limits_1^2y^2dx$$

5. Fey

The shell method uses the 2(pi) at the beginning. Can u explain how u got that answere?

6. klimenkov

Yes. You have to understand what integral means. This solid consists of many little cylinders like on the pic|dw:1360448107971:dw| The volume of the cylinder is $$\pi R^2h$$, on the pic $$R$$ is $$y(x)$$ and $$h$$ is $$dx$$. We want the whole solid, so we sum the volumes of this small cylinders and get the volume of the solid as an integral.

7. Fey

well,,, im still not getting the right answere. its suppoased to be (pi)/2....

8. klimenkov

You have to calculate the integral I wrote correctly.

9. Fey

Oops. I made a mistake xD Ok, got it thanks.

10. klimenkov

You are welcome.

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