Question

\[ \int_{-a}^{a}|x|\,dx= \]

• A. \(a\)
• B. \(2a\)
• C. \(0\)
• D. \(a^2\)

Hint:

If \(f(x)\) is even, then \(\int_{-a}^{a}f(x)\,dx=2\int_0^a f(x)\,dx\).

Answer 1

The Correct Option is D

Step 1: Since \(|x|\) is an even function: \[ \int_{-a}^{a}|x|\,dx=2\int_0^a x\,dx \]

Step 2: \[ 2\int_0^a x\,dx = 2\left[\frac{x^2}{2}\right]_0^a \]

Step 3: \[ =2\cdot \frac{a^2}{2} \] \[ =a^2 \] \[ \boxed{a^2} \]