Area between curves

  • Thread starter Jeff Ford
  • Start date
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
 
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Using my calculator I get that their intersection is at [tex]x\approx1.646[/tex].
 
How did you manipulate the equation to calculate the answer? Or did you just use Newton's method?
 
Last edited:
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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.
 
Thanks for the help. I'm still getting used to the idea that most equations are unsolvable.
 
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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