Question

Using method of integration find the area surrounded by lines 2x+y+4, 3x-2y=6, x-3y+5+0

Answer 1

Dear Friend,
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Here's what you were looking for:

By plotting the three lines on the graph, we get the intersection point as (1,2),(2,0) and (4,3).

So the required area is

∫₁⁴ (x+5)/3 - ∫₁² 2x-4 - ∫₂⁴(3x-6)/2

=11/2 sq. units

I had attached the graphs of three lines.
Red: 2x+y=4
Blue: 3x-2y=6
Green: x-3y+5=0

Hope this clears your doubt. ✌️

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Answer 2

Please see the attachment