Question
Using integration, find the area of the triangular region whose sides have the equations y = 2 x + 1, y = 3 x + 1 and x = 4.
Solution
The equations of the sides are
y = 2 x + 1 ...(1)
y = 3 x + 1 ...(2)
and x = 4. ...(3)
Subtracting (1) from (2), we get,
Putting x = 0 in (1), we get y = 0+1 = 1
line (1) and (2) intersect in A(0, 1)
From (1) and (3), we get,
line (1) and (3) intersect in B (4, 9)
From (2) and (3), we get,
x = 4, y = 12 + 1 = 13
∴ lines (2) and (3) intersect in C (4, 13)
∴ vertices of the triangle ABC are A(0, 1), B (4, 9), C (4, 13)
Required area = Area of ∆ ABC = Area of region AOMC - area of region AOMB
