GATE 2020 MT – Question 31

Engineering Mathematics · Calculus and vector calculus · 1 mark · Numerical answer

For f(x) shown, find $\int_0^1[1-f(x)]\,dx$, rounded to 1 decimal place.

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Show answer and explanation

Correct answer: 0.5 to 0.5

Explanation

The plotted line runs from (0,0) through (0.5,0.5) to (1,1), so f(x) = x on [0,1]. Therefore $\int_0^1(1-x)dx=[x-x^2/2]_0^1=0.5$. Geometrically it is the triangular area above the diagonal in a unit square.

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