Thread: Integration General Wonder

1. Integration General Wonder

Say given a semi-circle, the region is boudned by the x axis, and a solid of revolution is formed by rotation across the y axis. Then a solid of revolution is formed using also the given semi circle but bounded by both the x-axis and y-axis, and then rotated across the y axis. What is the difference in area?

Since by visualising the solid formed, there wouldnt be a difference since the solid formed is the same. IS that correct? Or am i visuallising something wrong?

2. Originally Posted by Lukybear
Say given a semi-circle, the region is boudned by the x axis, and a solid of revolution is formed by rotation across the y axis. Then a solid of revolution is formed using also the given semi circle but bounded by both the x-axis and y-axis, and then rotated across the y axis. What is the difference in area?

Since by visualising the solid formed, there wouldnt be a difference since the solid formed is the same. IS that correct? Or am i visuallising something wrong?
if I understand your query correctly ...

rotation of the plane region
$\displaystyle y = \sqrt{r^2 - x^2}$ about the y-axis yields a solid hemisphere of radius $\displaystyle r$.

restricting the plane region to be rotated to that in quadrant I yields the same result.

3. The only difference being that with the semi-circle, you only have to rotate through 180 degrees to sweep out the entire volume while with the quarter circle you have to rotate throught 360 degrees.