# C4 Integration Help - VolumesWatch

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#1
Am a bit stuck on this question.

The Curve C has parametric equations
x = sint, y = sin2t, 0<t<Pi/2

If this region is revolved through 2Pi radians about the x-axis, find the volume of the solid formed.

If anyone can guide me through this it would be appreciated
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13 years ago
#2
(Original post by martinkings)
Am a bit stuck on this question.

The Curve C has parametric equations
x = sint, y = sin2t, 0<t<Pi/2

If this region is revolved through 2Pi radians about the x-axis, find the volume of the solid formed.

If anyone can guide me through this it would be appreciated
V=pi int y^2 dx = pi int y^2 dx/dt dt
= pi int sin^2 2t cost dt
= pi int 4sin^2t 4cos^3t dt
= pi int 16 sin^2t (1-sin^2t) cost dt
= pi int 16sin^2 t cost dt - pi int 16 sin^4 t cost dt
You know that int sin^(a) t cost dt = 1/(a+1) sin^(a+1) t + C using integration via substitution, so you can easily evaluate the two above integrals.
Note that I've neglected writing the limits, which you need to apply.
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