Answer: 3(pi - 2)/2.
- A 3(pi - 2)/2
- B 3pi - 6
- C pi - 2
- D 6(pi - 2)
Correct answer: A. 3(pi - 2)/2
Explanation: Using the standard NCERT technique (integrating the ellipse boundary minus the line, from x=0 to x=3), the smaller region's area simplifies to 3(pi-2)/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.