Using the method of integration find the area of the region bounded by lines:`2x + y = 4, 3x 2y = 6`and `x 3y + 5 = 0`

Explanation

The given equations of lines are

`2x+y=4.........(1)`

`3x−2y=6.........(2)`

And, `x−3y+5=0..........(3)`

Area`(ΔABC)=Area(ALMCA)−Area(ALB)−Area(CMB)`

`=int_1^4​(x+5​)/3dx−int_1^2​(4−2x)dx−int_2^4​(3x−6​)/2dx`

`=1/3​[(x^2)/2​+5x]​−[4x−x^2]−(1/2)​[(3x^2)/2​−6x]`
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`=(1/3)​[8+20−1/2​−5]−[8−4−4+1]−1/2​[24−24−6+12]`

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