When drawing 3d shapes superimposed on 2d planes we sometimes rotate the axes to make the perspective clearer. In Example 9 I rotated the axes to give a better view of the wedge slice, and in Example 7 I drew the axes slanted to give the impression of the 3d solid coming out of the plane. Drawing the axes in their standard positions would suggest a top down perspective, which would make everything seem 2d.
for example 4 would it be possible to evaluate via dy. If it is possible then why did you chose to evaluate via the dx integral, is it all just preference?
In order to use a dy integral instead of dx for example 4 you would need to use the shell method, since using the disc/washer method produces washers with thickness Δx.
ooh i see why you put 2pi, but i dont understand at all why you put 0 in the integral, it is because you multiplied by 2 the integral, so now you dont have to take in to consideration the negative numbers, because youre just using now one side of the circle and then you multiply it by 2 to make the complete circle right?
Thank U
In exaple9, why is the y horizontal and x vertical? And also dont understand why the y axis is slanted in the example7.
When drawing 3d shapes superimposed on 2d planes we sometimes rotate the axes to make the perspective clearer. In Example 9 I rotated the axes to give a better view of the wedge slice, and in Example 7 I drew the axes slanted to give the impression of the 3d solid coming out of the plane. Drawing the axes in their standard positions would suggest a top down perspective, which would make everything seem 2d.
@@asherroberts thank u！
for example 4 would it be possible to evaluate via dy. If it is possible then why did you chose to evaluate via the dx integral, is it all just preference?
In order to use a dy integral instead of dx for example 4 you would need to use the shell method, since using the disc/washer method produces washers with thickness Δx.
in the example 1 in the part of the integral where and when did you get that 2pi and the 0 in the integral and how?
ooh i see why you put 2pi, but i dont understand at all why you put 0 in the integral, it is because you multiplied by 2 the integral, so now you dont have to take in to consideration the negative numbers, because youre just using now one side of the circle and then you multiply it by 2 to make the complete circle right?
Right
@@asherroberts i didnt understand in the example number 7 how did you get y= square root(1-x2)
i didnt understand too much things of that example to be honest, where you got square root(3y)
i understand how youre trying to explain the problem but i got completely lost trying to figure out where you get those values