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calculus

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Find circumference of the circle r=2acos theta.
s= Int (0 to 2pi) of Sqrt(4a^2cos^2 theta+4a^2sin^2 theta)d theta
=Int (0 to 2pi)2a*Int theta d theta
=2a(2pi-0)=4a*pi
Book shows 2a*pi. Am I wrong somewhere?

  • calculus - ,

    Sorry, slight typo. Please reasd it as Int (0 to 2pi)2a*Int d theta=2a(2pi-0)=4a*pi

  • calculus - ,

    well, you know from the equation that the circle has radius a, so its circumference is 2a*pi.

    r = 2acosθ
    r^2 = 2arcosθ
    x^2+y^2 = 2ax
    (x-a)^2 + y^2 = a^2

    Now, as for the integration, your formula is correct, but as θ goes from 0 to 2pi, the circle is traced twice. So, you should only integrate from 0 to pi.

    Do a plot and you can see why this is so.

  • calculus - ,

    Thanks a lot for guiding,please.

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