Science:Math Exam Resources/Courses/MATH101 C/April 2024/Question 17 (a)/Solution 1

We must find the $c$ such that

$${\begin{aligned}1&=\int _{-\infty }^{\infty }f(x)\;\mathrm {d} x=\int _{-1/2}^{0}1\;\mathrm {d} x+\int _{0}^{c}2\;\mathrm {d} x\\&={\frac {1}{2}}+2c.\end{aligned}}$$

The solution is $c=1/4$.