Question

The region bounded by y = tan(x), y = 0, x=pi/4 is rotated about the x-axis. The volume generated equals?

Answer 1

the sum of the areas of circles whose radius is equal to f(x)

\[\int \pi~r^2\]
\[\pi\int_{0}^{\pi/4} tan^2(x)~dx\]

Answer 2

\[\pi [(\sec^2(\pi/4)-1) -(\sec^2(0))] \] ?

Answer 3

tan^2 = sec^2 - 1


integrate gives us tan(x) - x, from 0 to pi/4 is just

tan(pi/4) - pi/4; or simply 1 - pi/4, times pi of course

Answer 4

got it! thank you so much!