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Question
Sketch the region bounded by the lines 2x + y = 8, y = 2, y = 4 and the Y-axis. Hence, obtain its area using integration.
Solution
2x + y = 8, y = 2, y = 4
Required Area = Area of ABDE + Area of BCD
= `int_0^2 (4 - 2)dx + int_2^3 {(8 - 2x) - 2}dx`
= `[2x]_0^2 + [6x - x^2]_2^3`
= 4 + [18 – 9 – 12 + 4]
= 4 + 1
= 5 sq. units.
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