Using integration find the area of region bounded by the triangle whose vertices are (– 1, 0), (1, 3) and (3, 2).

Question

Using integration find the area of region bounded by the triangle whose vertices are ( 1, 0), (1, 3) and (3, 2).

Philoid · Accepted Answer

BL and CM are drawn perpendicular to x – axis.

We can see that from the figure that,

Area(ΔACB) = Area(ALBA) + Area(BLMCA) - Area(AMCA) …(1)

Now, equation of line segment AB is

Thus, Area(ALBA) =

Now, equation of line segment BC is

Thus, Area (BLMCB) =

Now, equation of line segment AC is

Thus, Area (AMCA) =

Now putting all these values in equation (1), we get,

Area(ΔABC) = (3 + 5 – 4) = 4 units.