If a function f(x) ≤ 0 on the interval [a, b], how is the geometric area bounded by y = f(x), the x-axis, x = a, and x = b correctly represented?

If a function f(x) ≤ 0 on the interval [a, b], how is the geometric area bounded by y = f(x), the x-axis, x = a, and x = b correctly represented?

• A. |∫(a to b) f(x) dx|
• B. ∫(a to b) f(x) dx
• C. ∫(b to a) f(x) dx
• D. Both |∫(a to b) f(x) dx| and ∫(b to a) f(x) dx

Answer: D) Both |∫(a to b) f(x) dx| and ∫(b to a) f(x) dx

Explanation: Since f(x) ≤ 0, the definite integral gives a negative value. We use the absolute value or reverse the limits to make it positive.