Could someone verify these integrals (no text )

[Saladsamurai]

Could someone verify these integrals (no text:()

I got these integrals wrong on a quiz I just took. Looking back, I am not quite sure what I was thinking:/ But I have reworked them and would like know if I have the integrals set up properly; I don't need to evaluate them...just set them up:

Set up the integral to find the Volume by Cylindrical Shells of the region enclosed by $$y=x^2$$ and $$y=x$$

rotated about:

x-axis: $$V=2\pi\int_0^1y(\sqrt{y}-y)dy$$

y-axis $$V=2\pi\int_0^1x(x-x^2)dx$$

and the region enclosed by y=2-x, y=x^2 in the 1st quadrant rotated around x=3: $$V=2\pi\int_0^1(3-x)(2-x-x^2)dx$$

I know these can be simplified, but I am not concerned with that, just the concept.

Thanks,
Casey

 

[Saladsamurai]

I would really appreciate if some one could verify these.

 

[bob1182006]

all 3 are correct.

 

[Saladsamurai]

Thanks bob. I have an Exam on Monday!

Casey