Question

The area of the region bounded by the curve y=x2 and the line y=16 is:

• A. (A) 323 sq.units
• B. (B) 2563 sq.units
• C. (C) 643 sq.units
• D. (D) 1283 sq.units

Answer 1

Answer: (B)

(B) 2563 sq.units

Answer 2

Explanation:
Given equation of curves arey=x2⋯(1)y=16⋯(2)By solving both equation (1) and (2),x2=16x=4,−4∴ Points of intersection are (4,16) and (−4,16).From the figure we have,Required Area =∫−44(16−x2)dxBy using Integral property,A=2∫04(16−x2)dx=2[16x−x33]04=2[16x−x33]04=2[64−643]=2×64×23A=2563 sq.unitsHence, the correct option is (B).