RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 18 of Exercise 21.3

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18

Find the area of the region bounded by by y = √x and x = 2y + 3 in the first quadrant and x - axis.

To find an area in the first quadrant enclosed by the x - axis

y = √x ...(i)


x = 2y + 3 ...(ii)


On solving the equation (i) and (ii),



y2 = 2y + 3


Or, y2 – 2y – 3 = 0


Or, (y – 3)(y + 1) = 0


Or, y = 3 or y = – 1


These are shown in the graph below: -



Required area of the bounded region



The area of the region bounded by by y = √x and x = 2y + 3 is


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