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GATE 2026 BT – Question 13

Engineering Mathematics · Calculus: Limits, continuity, differentiability, partial derivatives, maxima and minima · 1 mark · Multiple choice

Which of the following functions has the highest area under the curve between $x = 0$ and $x = 10$?

  1. $y = x + 8$
  2. $y = 3x$
  3. $y = 2x + 1$
  4. $y = x + 2$

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Correct answer: (B) $y = 3x$

Explanation

The areas are $\int_0^{10}(x + 8)dx = 130$, $\int_0^{10}3x\,dx = 150$, $\int_0^{10}(2x + 1)dx = 110$ and $\int_0^{10}(x + 2)dx = 70$. The largest is for $y = 3x$.