Question

If \(\int _a^b(x^2-x)\,dx = 18,\int _a^bx^3\,dx = 0\), then \(a+b\) is equal to

• A. \(3\)
• B. \(6\)
• C. \(0\)
• D. \(9\)

Hint:

Use the odd function property of f(x) sin x over a symmetric interval.

Answer 1

The Correct Option is C

Step 1: Geometric meaning:
The graph of $|x|$ on $[-2, 2]$ forms two right triangles with legs 2 and 2.

Step 2: Area:
Each triangle has area $\frac12\times2\times2 = 2$, so the total is 4. The odd part adds nothing, so the answer is 4 (B).

Final Answer:
4. \[ \boxed{4} \]