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Question

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

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Solution

Let the lines be,AB : x + 2 y = 2,
CA : y - x = 1 and BC : 2 x + y = 7
Points of intersection are A(0,1), B(4,-1) and C(2,3).
Required Area=1231(7y)dy11(22y)dy31(y1)dy


=12[7y12y2]31[2yy2]11[12y2y]31
= 1242=6 Sq.units.

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