Area under the curveMedium

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

Create a free account to view solution

View Solution Free
Topic: Area under the curve·Practice all Area under the curve questions

More Area under the curve Questions

The area between the curve y = ex and x-axis which lies between x = − 1 and x = 1 is-...The area bounded by the curves y = e|x|, y = e–|x| and |x| = 1, is-...The area enclosed between the curves y = loge(x + e) x = loge and the x-axis is equal to...The area bounded by the curves y = x(1 - lnx) and positive x-axis between x = e-1 and x = e is -...Suppose y = f(x) and y = g(x) are two functions whose graphs intersect at three points (0, 4), (2, 2) and (4, 0) with f(...