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Let S be the region in the xy-plane defined by y >= x² - 1 and y <= x + 1. Find the area of region S.

1. 4
2. 3/2
3. integral from 1 to 2 of floor(x) dx - 1/2
4. integral from 1 to 4 of floor(x) dx - 3/2

Correct answer: integral from 1 to 4 of floor(x) dx - 3/2

Solution

Area between line y=x+1 and parabola y=x²-1 from x=-1 to x=2 equals 9/2. The option integral(1 to 4) floor(x) dx - 3/2 = (1+2+3) - 3/2 = 6 - 3/2 = 9/2, confirming it as the answer.

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