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?
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].
Thank You. I think i got the idea. i will try to solve it.
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???
I apologize for any confusion caused by my previous response. Upon reviewing the question again, I can confirm that there are indeed missing limits, as the question only provides specific equations of the curves but does not provide the boundaries for the regions. Without the limits of integration, it is not possible to determine exact solutions for this problem.
To solve this question, you would need to know the limits that define the regions enclosed by the given curves. Please note that limits could be given in terms of x, y, or even a combination of both. These limits are essential to compute the definite integrals necessary for finding the areas and determining the value of c.
If the question you posted is all the information you have, it seems that some details are missing. It would be best to consult the original source or to provide additional context if available. Without the necessary limits, it is not possible to provide a specific solution to this problem.