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Find the area (in square units) of the region in the first quadrant bounded by the curves y = 2^x and y = |x + 1|.

1. 3/2 - 1/logₑ 2
2. 1/2
3. logₑ 2 + 3/2
4. 3/2

Correct answer: 3/2 - 1/logₑ 2

Solution

Both curves pass through (0,1) and (1,2); the area between y = x+1 and y = 2^x from 0 to 1 equals 3/2 - 1/ln 2.

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