IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

sowjanya_reddygudipati

given the slope of the curve at the points x=1,2,3

slope of the curve f(x)=f¹(x)

f¹(1)=1/root3, f¹(2)=root3, f¹(3)=1

let f¹(x)=t

then f¹¹(x)dx=dt

_{[ ]}

^{[ ]} f¹(x)f¹¹(x)dx=_{[ ]}

^{[ ]} tdt within the limits 1to3

=t²/2 with in the limits 1 to 3

=1/2(1-1/3)=1/3

_{[ ]}

^{[ ]} dt=t with in the limits 2to 3

=1-root3

1/3+1-root3=4/3-root3

f¹(x) is derivative of f(x)

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