For an odd function f(x), the integral ∫(−a to a) f(x) dx = 0. What does this imply about the geometric areas bounded by the curve and the x-axis on the intervals [−a, 0] and [0, a]?

For an odd function f(x), the integral ∫(−a to a) f(x) dx = 0. What does this imply about the geometric areas bounded by the curve and the x-axis on the intervals [−a, 0] and [0, a]?

• A. They are equal in magnitude but opposite in sign.
• B. Both areas are geometrically zero.
• C. The curve does not exist on this interval.
• D. The area cannot be determined.

Answer: A) They are equal in magnitude but opposite in sign.

Explanation: Odd symmetry means the region below the axis perfectly mirrors the region above the axis, causing the signed areas to sum to zero.