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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
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
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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