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Ex 4: Find the volume of the solid obtained by rotating the region bounded by \(\displaystyle y = x - x^2 \)and \(\displaystyle y = 0\) about the line \(\displaystyle x = 2\)

I did all the algebra, integrated etc etc. But I was thinking that the integral would be from \(\displaystyle \int^2_0\) since it says about the line \(\displaystyle x = 2\)..How do they get from \(\displaystyle \int^1_0\)? I'm almost positive it has to do with the fact that i am saying \(\displaystyle 2 - x\)...But how exactly do I know it's from \(\displaystyle \int^1_0\). I guess I see the mechanics of what is going on but I don't understand it, or maybe I don't see the mechanics at all and am lost in the dark..Any elaboration would be great.

I did all the algebra, integrated etc etc. But I was thinking that the integral would be from \(\displaystyle \int^2_0\) since it says about the line \(\displaystyle x = 2\)..How do they get from \(\displaystyle \int^1_0\)? I'm almost positive it has to do with the fact that i am saying \(\displaystyle 2 - x\)...But how exactly do I know it's from \(\displaystyle \int^1_0\). I guess I see the mechanics of what is going on but I don't understand it, or maybe I don't see the mechanics at all and am lost in the dark..Any elaboration would be great.

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