Answer: Integral of x dy from c to d.
- A Integral of x dy from c to d
- B Integral of y dx from c to d
- C g(d) - g(c)
- D Integral of g(y) dy from 0 to 1
Correct answer: A. Integral of x dy from c to d
Explanation: When integrating with respect to y, area = integral from c to d of x dy = integral from c to d of g(y) dy.
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.