1.

Let S is the region of points which satisfies y^(2)lt16x,x lt4 and (xy(x^(2)-3x+2))/(x^(2)-7x+12)gt0. Its area is

Answer»

`(8)/(3)`
`(64)/(3)`
`(32)/(3)`
none of these

Solution :`(xy(x^(2)-3x+2))/(x^(2)-7x+12)gt0`
`rArr""(xy(x-1)(x-2))/((x-3)(x-4))gt0`
`rArr""{{:(ygt0",","if",(x(x-1)(x-2))/((x-3)(x-4))gt0),(ylt0",","if",(x(x-1)(x-2))/((x-3)(x-4))lt0):}`
`rArr""{{:(ygt0",","if",x in(0,1)uu(2,3)uu(4,oo)),(ylt0",","if",x in(-oo,0)uu(1,2)uu(3,4)):}`
`y^(2)lt16x" is interior of the parabola "y^(2)=16x`
Region is as shown in the following FIGURE:

From the figure, required AREA
= HALF of the area of the region bounded by
`y^(2)=16x and x=4`


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