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Today's calculation of Integral 174

Source: Tokyo Institute of Technology entrance exam 1987

January 18, 2007
calculusintegrationgeometryparameterizationcalculus computations

Problem Statement

Let aa be a positive number. Assume that the parameterized curve C: x=t+eat, y=−t+eat (−∞<t<∞)C: \ x=t+e^{at},\ y=-t+e^{at}\ (-\infty <t< \infty) is touched to xx axis. (1) Find the value of a.a. (2) Find the area of the part which is surrounded by two straight lines y=0,y=xy=0, y=x and the curve C.C.
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