Question

Using method of integration find the area of triangular region whose vertices are (2,-2)(4,3)(1,2)

Answer 1

dear student

$$\begin{gathered} wesolvefortheequationofthreesidesoftriangle \\ sidethrough(1,2)and(4,3)isx-3y=-5 \\ sidethrough(1,2)and(2,-2)is4x+y=10 \\ sidethrough(2,-2)and(4,3)is5x-2y=14 \\ requiredarea \\ =areaoftriangle \\ =\left|{\int }_1^4\left(\frac{x+5}{3}\right)dx\right|-\left|{\int }_1^{3/2}\left(6-4x\right)dx\right|-\left|{\int }_{14/5}^4\left(\frac{5x-14}{2}\right)dx\right|+\left|{\int }_{3/2}^2\left(6-4x\right)dx\right|+\left|{\int }_{3/2}^{14/5}\left(\frac{5x-14}{2}\right)dx\right| \\ integratingthetermsandsolvingtheaboveequation,weget \\ area=13/2 \end{gathered}$$

regards