Calculus 1

(1 point) Write an expression for the function, f(x), with the properties. f′(x)=(ln(x)2)/x and f(3)=7.

f(x)=∫t=b
t=a

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  1. f′(x)=ln^2(x)/x
    let u=lnx and you have f'(x) = u^2 du
    f(x) = 1/3 ln^3(x)+C
    f(3)=7, so
    1/3 ln^3(3)+C = 7
    C = 7 - 1/3 ln^3(3)

    f(x) = 1/3 ln^3(x) + 7 - 1/3 ln^3(3) ≈ 1/3 ln^3(x) + 6.558

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