calculus

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Trig

    Solve the following interval 0<_ (less than or equal to)0(Theta)<2pi: 1. sin0(theta) + sin2 0(theta) = 0 2. 2cos^20 (theta) + cos0 (theta) -1 = 0
  2. Calculus

    I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure …
  3. pre calc

    find all solutions on 0 is greater than or equal to theta < 2pi cos theta= 2sqrt3/3 4-1/2sin theta= (-16+sqrt3)/4 3(sqrt3)= -3cot theta -2=-1-2sin theta
  4. math

    find all solutions on 0 is greater than or equal to theta < 2pi cos theta= 2sqrt3/3 4-1/2sin theta= (-16+sqrt3)/4 3(sqrt3)= -3cot theta -2=-1-2sin theta
  5. Precalculus check answers help!

    1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.) Simplify …
  6. Precalculus check answers help!

    1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.) Simplify …
  7. math

    knowing that 2(theta) can be written as theta + theta, find the expression for sin2(theta) and cos2(theta). Is it 2sin(theta)cos(theta)?
  8. calculus

    Find complete length of curve r=a sin^3(theta/3). I have gone thus- (theta written as t) r^2= a^2 sin^6 t/3 and (dr/dt)^2=a^2 sin^4(t/3)cos^2(t/3) s=Int Sqrt[a^2 sin^6 t/3+a^2 sin^4(t/3)cos^2(t/3)]dt =a Int Sqrt[sin^4(t/3){(sin^2(t/3)+cos^2(t/3)}]dt=a …
  9. Math Trig Please Help!!!

    Find exact values for all the solutions to the equation cos theta = sqrt 3/2 for -2pi <= theta <= 2pi Theta = Theta = Theta = Theta =
  10. Algebra2

    The function f(theta) and g (theta) are sine functions where f(0)=g(0)=0. The amplitude of f (theta) is twice the amplitude of g(theta). The period of f(theta) is one-half the period of g(theta). If g (theta) has a period of 2pi and …

More Similar Questions