Question:

78. $\int |x| dx$ is equal to

(a) $\frac{x^2}{2} + C$

(b) $-\frac{x}{2} + C$

(c) $x|x| + C$

(d) $\frac{1}{2}x|x| + C$

Step-by-Step Solution

Key Concept: The absolute value function must be handled by considering cases: for $x \geq 0$, $|x| = x$; for $x < 0$, $|x| = -x$.

Solution not provided in the source text.

Correct Answer: D