Eduprobe
Question:
Let A = {(x,y): y² ≤ 4x, y ≥ -2x}. The area (in square units) of the region A is:
9
10
8
11
Solution:
Point of intersection of parabola and line are (1,-2) and (4,4)
Required area=∫⁴₋₂(x₁-x₂)dy=∫⁴₋₂(y²/4)dy-∫⁴₋₂(1/2)(y+4)dy=[y³/12]⁴₋₂-[y²/2+4y]⁴₋₂=6-7=-1Area = 9 sq.units