Let f(x) = max |x + 1|, |x + 2|, ......., |x + 5| . Then _ -6 ^0f(x)dx is equal to _____.

JEE Main 2022 Mathematics question

Mathematics Application of Derivatives JEE Main 2022

Let f(x) = max{|x + 1|, |x + 2|, ......., |x + 5|}. Then is equal to .

Answer: 21

Solution

The maximum of the |x + k| is |x + 5| for −3 and |x + 1| for −3 (the two outermost lines dominate), with f(−3) = 2. So f is the V-shaped function: on [−6, −3] it equals |x + 1| = −(x + 1)

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Question ID VK-025367