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Homework Help: Area between curves

  1. Apr 18, 2006 #1
    Write, but do not evaluate the integral that will give the area between [tex] y = cos x [/tex] and [tex] y = x/2 - 1 [/tex], bounded on the left by the y-axis

    I've sketched the graphs, so I know that [tex] y = cos x [/tex] is above [tex] y = x/2 - 1 [/tex], so the indefinite integral to solve would be [tex] \int (cos x) - (x/2 -1) dx [/tex]

    I know the lower bound is zero, since it's bordered by the y-axis, and I know that to find the upper bound I need to find the point of intersection of the two curves.

    The professon told us to use "technology", which usually means Mathematica. I can't seem to get Mathematica to solve the equation [tex] cos x = x/2 - 1 [/tex]

    Any advice on either how to get Mathematica to solve such an equation, or another method of finding the point of intersection?

    Thanks
    Jeff
     
  2. jcsd
  3. Apr 18, 2006 #2
    Using my calculator I get that their intersection is at [tex]x\approx1.646[/tex].
     
  4. Apr 18, 2006 #3
    How did you manipulate the equation to calculate the answer? Or did you just use Newton's method?
     
    Last edited: Apr 19, 2006
  5. Apr 19, 2006 #4
    I just used my calculator. I don't believe that this can be solved for explicitly. Newton's Method would work, but I graphed it on my TI-89 and found the intersection point.
     
  6. Apr 19, 2006 #5
    Thanks for the help. I'm still getting used to the idea that most equations are unsolvable.
     
  7. Apr 20, 2006 #6
    You can graph it on any graphing calculator and use the ISECT (intersect) function to find where they interstect, and that's your x value solution.

    So you'd have:
    y1 = cosx
    y2= x/2 -1
     
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