RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 21 of MCQ

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21

Area enclosed between the curve y2 (2a – x) = x3 and the line x = 2a above x-axis is

y2(2a – x) = x3




Since we are concerned with the area above the x – axis, we’ll be considering the positive root.


We can see that at x = 0, y = 0.


So,


A =


Putting √x = u


We get du = (1/2√x)dx


or, dx = 2u du


So,


A =


Putting u = √2√a sin t


We get du = √2√a cos t dt


A =


=


=


=


=


=


=


=


=


= 4a2(π/2 – 0 – 0 + 0) – a2(π/2 – 0 – 0 + 0)


= πa2 (Ans)

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