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Area bounded by f(x)=(x-1)(x+1)/(x-2), the x-axis and the ordinates x=0 and x=1.5 is (a) 4/5 sq unit (b)7/8 sq unit (c) 1 sq unit (d) none of these

Area bounded by f(x)=(x-1)(x+1)/(x-2), the x-axis and the ordinates x=0 and x=1.5 is


(a) 4/5 sq unit


(b)7/8 sq unit


(c) 1 sq unit


(d) none of these

Grade:12

1 Answers

Ramesh V
70 Points
14 years ago

The curve has roots at x= -1 and +1 and x=2 is asymptote of f(x)

so, 0<x<1,   f(x) is positive

     1<x<1.2, f(x) is negative

f(x) can be simplified to:  f(x) = (x+2)  + 3/(x-2)

area bounded is : limits (0,1) f(x)  -  limits (1,1.5) f(x)

           Area = { integrating from (0,1) on:(x+2) + 3/(x-2) } - { integrating from (1,1.5) on:(x+2) + 3/(x-2) }

                  = x2/2 +2x +3.ln(x-2) |on (0,1) - x2/2 +2x +3.ln(x-2) |on (1,1.5)

                  = 2 - (9/8)

                  = 7/8 sq. units

--

regards

Ramesh

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