What does the definite integral of a function f(x) from 'a' to 'b' geometrically represent when f(x) is non-negative over the interval [a, b]?

The correct answer to the question "What does the definite integral of a function f(x) from 'a' to 'b' geometrically represent when f(x) is non-negative over the interval [a, b]?" is Option C: The area under the curve of f(x) from x=a to x=b.

The other options — A) The slope of the tangent line at x=a, B) The instantaneous rate of change, D) The perimeter of the region bounded by f(x) — are incorrect for this IB Exam Prep question. As explained above: Geometrically, the definite integral of a non-negative function between two points represents the area of the region bounded by the function's graph, the x-axis, and the vertical lines at those two p…