GATE 2022 ES – Question 52

Mathematics Foundation · Calculus · 2 marks · Numerical answer

Find area enclosed by $y=x$, $y=3\sqrt{x}$ and x=0,x=1, to one decimal.

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Correct answer: 1.5 to 1.5

Explanation

On[0,1],3√x≥x. Therefore area=$\int_0^1(3\sqrt{x}-x)dx=[2x^{3/2}-x^2/2]_0^1=2-.5=\mathbf{1.5}$ square units. The square root is multiplied by 3; it is not a cube root.

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