Find Area Btwn Curves: y=cosx & y=x/2-1

[Jeff Ford]

Write, but do not evaluate the integral that will give the area between $$y = cos x$$ and $$y = x/2 - 1$$, bounded on the left by the y-axis

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

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 $$cos x = x/2 - 1$$

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

Thanks
Jeff

 

[Jameson]

Using my calculator I get that their intersection is at $$x\approx1.646$$.

 

[Jeff Ford]

How did you manipulate the equation to calculate the answer? Or did you just use Newton's method?

 

[Jameson]

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.

 

[Jeff Ford]

Thanks for the help. I'm still getting used to the idea that most equations are unsolvable.

 

[freecorp777]

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