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Let C1 be the curve y = (x-1) e^x. A1 is the area of the region bounded by C1, the tangent to C1 at (1,0), and the y-axis. A2 is the area bounded by C1 and the coordinate axes in the fourth quadrant. Which statement is correct?

1. A1 > A2
2. A1 < A2
3. 2 A1 + A2 = 2
4. A1 + 2 A2 = 4

Correct answer: 2 A1 + A2 = 2

Solution

With A2 = e - 2 and A1 = 2 - e/2, the combination 2A1 + A2 = 4 - e + e - 2 = 2.

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