sssgggg2827 sssgggg2827
  • 02-12-2017
  • Mathematics
contestada

Find a formula for the function f(x) such that f′(x)=(ln(x))^2/x and f(2)=6

Respuesta :

chudung1976
chudung1976 chudung1976
  • 02-12-2017
f(x)= ∫ln²x/x dx= ∫ln²xd(lnx) cause d(lnx)= (lnx)'dx=1/x dx
= ln³x/3 +C with C is constant
In addition, we have f(2)=6, so we have 6=ln³2/3+C
or C= 6- ln³2/3
And f(x)= 
ln³x/3+  6- ln³2/3
Answer Link

Otras preguntas

A large piece of jewelry has a mass of 132.6 g. A graduated cylinder initially contains 48.6 mL water. When the jewelry is submerged in the graduated cylinder,
92 liters in 4 minutes = liters per minute
10 13/14 - 3 4/7 Subtract. Simplify your answer and write it as a mixed number.
What is the y-intercept of the line with slope -2 that passes through (3, 1)?
Find one word that can be used in all 3 sentences Don't put anything heavy on top. The structure is too_____ to support it. World leaders are worrying that the
determine weather the two figures are similar. Explain your reasoning.​
Mother gave each of her children 1/16 of a cake. She then sold the remaining one-fourth of the cake. How many children does mother have? ​
What is the point of view in the excerpts from Olaudah Equiano’s memoir?
Ms. Hernandez gave her students a math test a with 42 questions. If Charlie got 36 questions right, what percent of the questions did he answer correctly?
What is energy and how is it conserved?