Question

Let R be the first quadrant region bounded by the lines y = x, y = 4x, and the hyperbolas xy = 1 and xy = 4. Calculate the area of R

Answer 1

a. Sola Given sata: R is a the first quadrant region bounded by ** y = 40 29=42 my! xy=4 and my = 4 Here, the co-ordinates of points of intersection de 645 A(1,1), B(1:2), C(1,4) and D (2,2). [(*) The intersecting points are found out from the given equations above} Join BD and def divide the region R into two parts. In the region ABD of R, y varies from y=1 to y=x, and a varies from n=1 to x=2. In the region BCD of R, y varies from y=4x to y = 1 / 2 and a varies from u = 1/2 to x=l. Now, Area of region R = Area of region ABD + Area of region BCD. in & 1 dyda. ť 4 2 x - dya 2

(-) de + $(4-one) dhe [$- mes* 4 (16- (12-16)- £+00) +4[men- 4 - 4)+"] - [2 – 1n(0) --1]+4[-3 - ($) + 1] = -0.693 - } -$+0.693x4 + Ž 2 = 3*0.693 - 2.0794 square units.

The problem is solved and provided above.

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