Area under the curveHard

Question

Area bounded by the curves y = and √y = |x - 1| is -

Options

A.2( - (x - 1)2)dx
B.2(√x - x2) dx
C.2(- (2-x)2)dx
D.

Solution

       
y = and √y = |x - 1|
both curves intersect at (0, 1), (1, 0) and (2, 1)
required area = 2 (y2 - y1) dx
⇒ ⇒ A = 2[ - (x - 1)2]dx ...... (1)
= 2
Apply f(x)dx = f(a + b - x)dx in (1)
⇒ A = 2[-(2 - x)2]dx
Required area can also be calculated as
2(y4 - y3)dx
= 2[-
(x - 1)2]dx
Apply f(x)x = f(a + b - x)dx
⇒ A = 2 [√x - x2]dx

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