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What do you mean? I'm a newbie so please specify and clarify

Yeah, I meant that those two questions' answers are the same. So is what I have established wrong?

(EDITED) 1. Use the shell method to find the volume of the solid generated by revolving about the y-axis. x=y^2, x=y+2 2. same as #1, except change y and x for the two equations and revolve about x-axis. I tried doing 2pi\int_{x=0}^4(x)(\sqrt{x}-x+2)dx but the answer is off for #1. I...

I made many typos... for number 2, it is actually rotated about the x-axis... for the second integral, it's not x there, it's supposed to be y... I edited the original post

Yes. Thank you. I have posted another question this time regarding shell method

(EDITED) 1. Use the shell method to find the volume of the solid generated by revolving about the y-axis. x=y^2, x=y+2 2. same as #1, except change y and x for the two equations and revolve about x-axis. I tried doing 2pi\int_{x=0}^4(x)(\sqrt{x}-x+2dx but the answer is off for #1. I tried...

Yes. How in the world did I get that equation? That is so wrong... It is so obvious for the isosceles right triangle to have two angles same... However, according to your answer, y2-y1 = 4-x &\int_{x=0}^4(1/2)(4-x)^2 This is wrong. (4-x)^2 is supposed to be hypotenuse so the correct...

The base of a solid is the triangular region bounded by the y-axis and the lines x + 2y = 4, x - 2y =4. Find the volume of the solid given that the cross sections perpendicular to the x-axis are isosceles right triangles with hypotenuse on the xy-plane. So what I did is: 2\int_{x=0}^2...

Yes. made some calculation error

But, I am not getting 512/15.

so A(x) = (4-x2)2 ? 2\int(4-x2)2dx (x is 0~2)

Thank you for the picture, but I do understand how it looks... just don't know how it goes with the integrals...

That's more confusing... can you explain it with integrals?

The questions: the base of a solid is the region bounded y=x^2 and y=4. Find the volume of the solid given that the cross sections perpendicular to the x-axis are squares. The answer is 512/15. I set A(x)= (2y)^2 = 4(x^2)^2=4x^4, and the answer is wrong when I integrate this from x = -2 to x =...

I understand that these inequalities actually do 'work', but what I do not understand is how you 'approach' these questions. Like, I understand the concept of upper and lower sums, but how do I come up with the inequalities in the first place? Do I need to first solve the integral by...