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Integral Calculus

Blazing goIITian

Joined:	11 Jun 2007
Post:	914

28 Oct 2007 10:19:54 IST

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267

Arrre, its area !!

None

Area enclose by (y-sin^-1 x)² = x-x² is equal to ?

answer : pi/4

yaar, how to plot the grrrraph..

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Priyesh

Blazing goIITian

Joined: 18 Feb 2007

Posts: 1042

28 Oct 2007 12:17:23 IST

Like 3 people liked this

for the equation to be valid

r.h.s must be greater than or equal to zero

hence x - x^2 >= 0

=> x lies between [0,1]

now the equation can be expanded as

y² -2ysin^-1x + (sin^-1x)² + x(x-1) = 0

now this is a quadratic in y

so y = f(x) form can be written

D = 4(sin^-1x)² - 4(sin^-1x)² +4(x(1-x)) = 4x(1-x)

so y = [2sin^-1x

2root(x(1-x))] / 2 = sin^-1x root(x(1-x))

now integrate this expression from 0 to 1 to get the answer

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