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Calculus - MathMate Please help

I asked this question on last thursday and u told me that the bottom limit for the 1st and the right limit for the 2nd area is missing? The question that i posted had no other information and i don't know why you said that the limits are missing. There is no other limits that are givin in this question. Does this question even have a limit? I don't know. I'm very confused now. I need help on this question. Please Help. Thank you.

Q. Suppose that 0 < c < pi/2. For what value of c is the area of the region enclosed by the curves y = cos x, y = cos(x - c), and x = 0 equal to the area of the region enclosed by the curves y = cos(x - c), x = pi, and y = 0?

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K

  1. Thank you for reposting.

    I must have misinterpreted the question, but a sketch of the curves made it crystal clear:
    http://img406.imageshack.us/img406/1995/1291016654.png

    We have two distinct areas enclosed by:
    1. cos(x), cos(x-c),and x=0
    2. cos(x-c), cos(x) and x=π
    The y=0 in the second area is extraneous and misleading for someone (like me) who hasn't taken the time to make a proper sketch.

    Now for the limits for each of the areas,
    1. from -π+c/2 to x=0
    2. from c/2 to π

    We are able to find the limits because of the symmetry of the curves cos(x) and cos(x-c).

    Finally, the integrals:
    1. ∫(cos(x)-cos(x-c))dx
    2. ∫(cos(x-c)-cos(x))dx

    Hope this will get you along the way.

    Hint: integrate and find each of the areas, equate the two areas and solve for c [if necessary].

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    MathMate

  2. Thank You. I think i got the idea. i will try to solve it.

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    K

  4. I got two areas but i cant solve it for c because they cancel each others out!!!

    the integral for the first one i got is [sin(c)cos(x)-cos(c)sin(x)+sin(x)+c]
    and
    the integral for the 2nd one i got is [-sin(c)cos(x)+cos(c)sin(x)-sin(x)+c]

    I don't know what to do from here. can u pleses help???

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    K

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