172
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=12∫3−1(7−y)dy−∫1−1(2−2y)dy−∫31(y−1)dy
⇒ =12[7y−12y2]3−1−[2y−y2]1−1−[12y2−y]31
⇒ = 12−4−2=6 Sq.units.
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=12∫3−1(7−y)dy−∫1−1(2−2y)dy−∫31(y−1)dy
⇒ =12[7y−12y2]3−1−[2y−y2]1−1−[12y2−y]31
⇒ = 12−4−2=6 Sq.units.
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