Question

Using integration, find the area of the triangle ABC with vertices as A(–1, 0), B(1, 3) and C(3, 2).

Answer 1

We mark the points on the graph and get the triangle ABC as shown in the figure

Required area of triangle = area of DABD + area of trapezium EDEC – area of DACE

Equation of line AB ⇒ y = \(\frac 32\)(x + 1)

Equation of line BC ⇒ y = \(-\frac x2+\frac 72\)

Equation of line AC ⇒ y = \(\frac x2+\frac 12\)

\(\therefore\) Area of