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what is the answer of the given question,in the picture uploaded??

what is the answer of the given question,in the picture uploaded??
 

Question Image
Grade:11

1 Answers

Aditya Gupta
2075 Points
2 years ago
y= x^2/a^2*sqrt(2ax – x^2)=  x^2/a^2*sqrt(a^2 – (x – a)^2)
to find the area we integrate y from points where y equals zero which are x=0 and x=2a. note that this integral can be solved by putting x – a=y and then using standard results for integrals of sqrt(a^2 – y^2) and y*sqrt(a^2 – y^2). however, for y^2*sqrt(a^2 – y^2) you will have to put y= asinz and it will turn into integral of sin^2z*cos^2z= (sin2z)^2/4. now put 2z=u and write sin^2u= (1 – cos2u)/2. 
on integrating the above term you shall find it is 5pia^2/8
now divide it by pia^2
so ratio equals 5/8
kindly approve :)

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