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Find the area bounded by the lines y=4x+...

Find the area bounded by the lines `y=4x+5, y=5-x" and "4y=x+5`.

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Given equations of lines are
`y=4x+5 …(i)`
`y=5-x …(ii)`
and `4y=x+5 …(iii) `
On solving Eqs.(i) and (ii), we get
`4x+5=5-x`
`rArr x=0`
On solving Eqs. (i) and (iii), we get
`4(4x+5)=x+5`
`rArr 16x+20=x+5`
`rArr 15x=-15`
`rArr x=-1`
On solving Eqs. (ii) and (iii), we get
`4(5-x)=x+5`
`rArr 20-4x=x+5`
`rArr x=3`
`:. "Required area "=int_(-1)^(0)(4x-5)dx+int_(0)^(3)(5-x)dx-1/4int_(-1)^(3)(x+5)dx`
`=[(4x^(2))/2+5x]_(-1)^(0)+[5x-(x^(2))/2]_(0)^(3)-1/4[x^(2)/2+5x]_(-1)^(3)`
`=[0-2+5]+[15-9/2-0]-1/4[9/2+15-1/2+5]`
`3+21/2-1/4 .24`
`3+21/2=15/2" sq units"`
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