Question

Let
f(x)=max\left\\{|x+1|,|x+2|,……,|x+5|\right\\}
Then $\int_{-6}^{0} f(x) \, dx$
is equal to_______

Answer 1

The correct answer is 21

Fig.

$\int_{-6}^{0} f(x) \, dx = 2 \left[ \frac{1}{2}(2 + 5) \cdot 3 \right] = 21$