GATE 2022 BM – Question 2

On 0≤x≤1, y(x)=2 for 0≤x<1/3, y(x)=3 for 1/3≤x<3/4, and y(x)=1 for 3/4≤x≤1. Find the area under the curve.

Show answer and explanation

Correct answer: (C) 13/6

Explanation

Sum the three rectangular areas: 2×(1/3)+3×(3/4−1/3)+1×(1−3/4)=2/3+5/4+1/4=13/6. Endpoint choices do not affect the integral. Therefore C.

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