Answer: Find the points of intersection of the curves.
- A Immediately integrate without checking which curve is on top
- B Find the points of intersection of the curves
- C Assume the answer is zero
- D Skip sketching the curves
Correct answer: B. Find the points of intersection of the curves
Explanation: Finding the intersection points first establishes the correct limits of integration and shows which curve lies above the other in each region.
The definite integral ∫ₐᵇf(x)dx computes the exact area of the shaded region bounded by the curve, the x-axis, and the vertical lines x=a and x=b - the same idea behind the Riemann sum, but evaluated exactly rather than approximated by rectangles.
Concept context
Using definite integrals to compute the area under a curve, the area between two curves, and the areas enclosed by standard curves like circles, parabolas, and ellipses.