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C4 integration - Area and Volume

The curve C has parametric equations x = sint, y = sin2t
t = 0 or 0.5pi

a) Find the area of the region bounded by C and the x axis

If this region is revolved through 2pi radians about the x axis,
b) Find the volume of the solid formed

(edited 13 years ago)

Reply 1

ztibor

Original post by Claxxy

for a) The area

\displaystyle \int^{\frac{\pi}{2}}_0 sin2t\ d(sint) =\int^{\frac{\pi}{2}}_0 2sintcost\cdot cost\ dt =-2\int^{\frac{\pi}{2}}_0 -sint\cdot cos^2t\ dt

So it is -2cos^3(t)/3 from 0 to pi/2

for b)

\displaystyle V=\pi \int^{\frac{\pi}{2}}_0 sin^22t\ d(sint)=\pi \int^{\frac{\pi}{2}}_0 4sin^2tcos^2t\cdot cost\ dt= 4\pi \int^{\frac{\pi}{2}}_0 (1-cos^2t)\cdot cos^3t\ dt

(edited 13 years ago)

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C4 integration - Area and Volume

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