So I have a problem with finding theta. I can always see from where to where the theta is going. The problem occurs when calculating volumes. Sometimes in the solutions book, for the full circle

$$4\int_0^{\pi/2} \ d \theta$$

is used (sometimes $8$ instead of $4$) and sometimes

$$\int_0^{2\pi} \ d \theta$$

How can i be sure which one to use? I understand that for the first one it is taking four times the first octant above $xy$ plane but why isn't the same thing done for the second one also. It changes the result when $0\rightarrow 2π$ is used if inside the integral there is $\sin \theta$ somewhere yet in solutions it is sometimes one sometimes the other. Please answer this as soon as possible.

  • $\begingroup$ Specific examples may help us answer your question more definitively. Please give us as much context as possible! $\endgroup$ – Cameron Buie May 19 at 23:41

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