Answer: 2.
- A 0
- B 1
- C 2
- D 4
Correct answer: C. 2
Explanation: cos x is positive on [0,pi/2] and negative on [pi/2,pi]. Area = |integral 0 to pi/2 of cos x dx| + |integral pi/2 to pi of cos x dx| = |1| + |-1| = 2.
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.