The graph looks like this, and I see 2 different regions
in quadrant I bounded by the two curves.
www.wolframalpha.com/input/?i=plot+y+%3D+tanx+,+y+%3D+2cosx+from+0+to+%CF%80%2F2
- which one do you want
- you did not specify the line of rotation, e.g. the x-axis? the y-axis?
You will need their intersection
tanx = 2cosx
sinx/cosx = 2cosx
sinx = 2cos^2 x
sinx = 2(1 - sin^2 x)
sinx = 2 - 2sin^2 x
2sin^2 x + sinx - 2 = 0
sinx = (-1 ± √17)/4 = .78078 or -1.28... <---- not in quad I
This should get you going, once you decide what your rotation is
Find the volume of the solid obtained by rotating the region in the first quadrant enclosed by the curves y= tanx and y=2cosx between the bounds 0 and pi/2.
I need the setup.
3 answers
its around y=-1
then what do i do?
then what do i do?
would it be
A= pi * ∫ 0 to 0.78 {(2cosx+1)^2 - (tanx+1)^2}
A= pi * ∫ 0 to 0.78 {(2cosx+1)^2 - (tanx+1)^2}