RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 40 of Exercise 21.3

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40

Find the area of the region bounded by the curve y = √1 – x2, line y = x and the positive x - axis.

To find the area of the region bounded by

y = √1 – x2 …(i)


X2 + y2 = 1


X = y …(ii)


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


Or X2 + x2 = 1


Or 2X2 = 1


Or x =


Equation (i) represents a circle (0,0) and meets axes at (±1,0), (0,±1).


Equation (ii) represents a line passing through B and and they are also points of intersection.


These are shown in the graph below:



Required area = Region OABO


= Region OCBO + Region CABC








The area of the region bounded by the curve y = √1 – x2, line y = x is


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