Question

what is the antiderivative of the volume of a sphere?

Answer 1

i am guessing with respect to its radius.
V = 4/3 pi r^3

\[\int\limits_{}^{}V dV = \frac{ 4 \pi }{ 3 } \int\limits_{}^{} r^3 dr= \frac{ 4 \pi }{ 3 }*\frac{ r^4 }{ 4 } = \frac{ \pi r^4 }{ 3 }\]

Answer 2

thanks. i was actually wondering as in a measurable term. Like the derivative of volume is surface area right?

Answer 3

sorry i wasn't very clear