Area between curves

  • Thread starter Jeff Ford
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  • #1
154
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
 

Answers and Replies

  • #2
789
4
Using my calculator I get that their intersection is at [tex]x\approx1.646[/tex].
 
  • #3
154
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How did you manipulate the equation to calculate the answer? Or did you just use Newton's method?
 
Last edited:
  • #4
789
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.
 
  • #5
154
1
Thanks for the help. I'm still getting used to the idea that most equations are unsolvable.
 
  • #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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