RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 20 of MCQ

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20

The area bounded by the curve y = 4x – x2 and the x-axis is

y = 4x – x2


This is a parabola with negative co-efficient of x2, i.e., it’s a downward parabola.


So, area A enclosed is the area of the peak of the parabola above the x – axis.


We need to find the bounds of this peak.


Now, at the point where the peak starts/ends, y = 0,


i.e., 4x – x2 = 0


x(4 – x) = 0


x = 0 or x = 4


A =


=


= [32 – 64/3]


= 32/3 sq. units (Ans)

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