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Find the area bounded by the parametric curve $x = \cos(t)$, $y = e^t, 0 < t < \pi/2$, and the lines $y = 1$ and $x = 0$.

I do not even know where to start with this problem. I know that I need to draw a graph, but that's all I know. Thanks for the help!

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How would I set up the definite integral? –  Ryan Nov 2 '12 at 4:41
when you say and the lines $y=1$ and $x=0$, do you mean "at" the lines $y=1$ and $x=0$ –  boby Nov 2 '12 at 4:44
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1 Answer

If $x=\cos(t)$, then $t=\arccos(x)$, at least when $0\leq t \leq \pi/2$. Thus, your curve can be expressed as $y=e^{\arccos(x)}$, which you can integrate over $[0,1]$.

I certainly agree that a picture like the one below is useful. You could plot both the parametric plot and the function plot using a tool like WolframAlpha. It then becomes apparent that you should subtract 1 from the integral. Of course, you can also ask WolframAlpha for help with the integral, which might be a bit tricky.

enter image description here

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why would you need to draw anything? evaluate the definite integral –  boby Nov 2 '12 at 4:36
@boby: What would the be the a and b values for the integral? –  Ryan Nov 2 '12 at 4:38
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