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Using the method of integration find th...

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`

Text Solution

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