Q. 203.7( 3 Votes )

Compute the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.

Answer :

Given;

The lines x + 2y = 2


x = 2 – 2y …. (1)


y – x = 1


x = y - 1 …. (2)


and 2x + y = 7 …. (3)



Equate the values of x from 1 and 2 to get,


2 – 2y = y – 1


2+1 = y + 2y


3 = 3y


y = 1


put the value of y in (2) to get,


x = 1 -1


= 0


So, intersection point is (0,1).


By solving these equations, we get the points of intersection as (0,1), (2,3) and (4,-1).


Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .


Required area





=3 + (24 − 12) − (12 − 3) = 6 sq.units


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