JEE Main 2022 · 26 Jun · Shift 1 · Mathematics Q24

MathematicsInteger+4 / -1Question 24 of 90

Let $f(x)=\max\{|x+1|,|x+2|,\dots,|x+5|\}$ . Then $\displaystyle\int_{-6}^0f(x)\,dx$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 21

The maximum. For $x\le-3$ the largest is $|x+1|$ ; for $x\ge-3$ it is $|x+5|$ .

Integrate. $\displaystyle\int_{-6}^{-3}|x+1|dx=\frac{25-4}2=10.5$ and $\displaystyle\int_{-3}^0(x+5)dx=\frac{25-4}2=10.5$ .

Total 21.

Answer: 21

JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 24