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area enclose between curves

Asked by imanumaan 18th April 2010, 1:48 PM
Answered by Expert
Answer:

y = |x|, will be y = x in first quadrant, and

x = y2 is a parabola.

Therefore they'll intersect in first quadrant only.

The intersection point is (1,1) as it only satifies y = x and x = y2.

The area inclosed between the curves, will be area under parabola from (0,0) to (1,1) LESS the area of right angled triangle with base as 1 unit and height as 1 unit.

Therefore, the area = [ydx] - (1/2)(1)(1)

= [x dx ] - 1/2            ... note that the limit for integration is 0 to 1, the limit for x.

= [x3/2/(3/2)] - 1/2

= 2/3 - 1/2 = 1/6  sq units.

Regards,

Team,

TopperLearning.

Answered by Expert 19th April 2010, 9:39 AM
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