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A function y(x) is defined in the interval [0, 1] on the x-axis as y(x) = { 2 if 0 ≤ x < 1/3 3 if 1/3 ≤ x < 3/4 1 if 3/4 ≤ x ≤ 1 } Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?

1. 5/6
2. 6/5
3. 13/6
4. 6/13

Correct answer: 13/6

Solution

Area = 2*(1/3) + 3*(3/4 - 1/3) + 1*(1 - 3/4) = 2/3 + 3*(5/12) + 1/4 = 8/12 + 15/12 + 3/12 = 26/12 = 13/6. The correct option is index 2, not the stored 5/6.

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