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Question
Find the area bounded by the lines y – 2x – 4 = 0, y = 0, y = 3 and the y-axis
Solution
The equation of the line given is y – 2x – 4 = 0
⇒ 2x = y – 4
⇒ x = `(y - 4)/2`
∴ x = `y/2 - 2`
Also y varies from 1 to 3
Required Area
A = `int_"a"^"b" x "d"y`
= `int_1^3 (y/2 - 2) "d"y`
= `[1/2 (y^2/2) - (2y)]_1^3`
= `[y^2/4 - 2x]_1^3`
= `[3^2/4 - 2(3)] - [(1)^2/4 - 2(1)]`
= `[9/4 - 6] - 41/4 - 2]`
= `(9/4 - 6) - (1/4 - 2)`
= `9/4 - 6 - 1/4 + 2`
= `8/4 - 4`
= 2 – 4
= – 2
Area can’t be in negative.
∴ Area = 2 sq.units
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