Science:Math Exam Resources/Courses/MATH101/April 2018/Question 01 (i)/Solution 2

Let $f(x)=1-2|x|$. Observe that it is an even function; $f(-x)=1-2|-x|=1-2|x|=f(x)$. Therefore, we have

$$\int _{-2}^{2}1-2|x|dx=2\int _{0}^{2}1-2|x|dx.$$

Evaluating the integral on the right hand side as in Solution 1, the given integral has the value $-4$, so the answer is $C$.

Answer: $\color {blue}C$