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# using integration find the area of the region bounded by the triangle whose vertices are (-1,2),(1,5) and (3,4).

Arun Kumar IIT Delhi
7 years ago
Hi
First draw the diagram then see the solution.
Its a simple application of straight lines and signs of area you get while integration.
$\\line_1 \\y=\frac{5-2}{1-(-1)}(x-1)+5 \\y=\frac{3}{2}(x-1)+5 \\line_2 \\y=\frac{5-4}{1-3}(x-3)+4 \\y=-\frac{1}{2}(x-3)+4 \\line_3 \\y=\frac{4-2}{3-(-1)}(x-3)+4 \\y=\frac{1}{2}(x-4)-3 \\Now \\Area=\int_{-1}^{1}(line_1-line_3)+\int_{1}^{3}(line_2-line_3)$