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The area bounded by the curve y=x^4-2x^3+x^2+3 , the axis of abscissas and two ordinates correponding to the points of minium of the function y(x) is

The area bounded by the curve y=x^4-2x^3+x^2+3 , the axis of


abscissas and two ordinates correponding to the points of minium of  the function y(x) is

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

f(x) = x4 -2x3 +x2 +3

f1(x) = 4x3 -6x2 +2x

on putting f1(x)=0

 x=0,1/2 ,1

now f2(x) =d2y/dx2 =12x2 -12x +2

f2(x) is +ve for x=0,1

hence its minimum is at x=0,1

now area bw curve and x=0,1 is

area =A= f(x)dx     limit 0 to 1

              =x5 /5 - x4 /2 + x3 /3 +3x       lim 0 to 1

               =91/30 square units

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