arewab arewab
  • 02-03-2017
  • Mathematics
contestada

If F(x)= integral from 0 to x of square root of (t^3 +1), then F'(2)=

Respuesta :

LammettHash
LammettHash LammettHash
  • 02-03-2017
By the fundamental theorem of calculus,

[tex]\displaystyle F'(x)=\frac{\mathrm d}{\mathrm dx}F(x)=\frac{\mathrm d}{\mathrm dx}\int_0^x\sqrt{t^3+1}\,\mathrm dt=\sqrt{x^3+1}[/tex]

which means

[tex]F'(2)=\sqrt{2^3+1}=\sqrt{8+1}=\sqrt9=3[/tex]
Answer Link

Otras preguntas

The Eightfold Path is a guiding principle of A) Buddhism. B) Christianity. C) Hinduism. D) Islam.
the outside diameter of a pipe is 5 and 7/32 inches. the wall of the pipe are 5/32 inches thick. find the inside diameter
When viewing a cork through his homemade microscope, Robert Hook discovered small compartments that he called _____. boxes cells prokaryotes eukaryotes
Which character from the play Antigone by Sophocles did the playwright use to create the climax of the play? Antigone Ismene Haemon Teiresias
Once the writer of a critical essay has read a novel carefully enough to say something sensible about it, the next step is
Who did Joan of Arc wish to crown as king of France at Reims? Edward III. Charles VII. Philip IV. Henry II.
Major organs form and cells continue to divide in the __________ stage.A.embryoB.fetusC.blastocystD.zygote
Clothing often showed to which segment of society a person belonged. True or False
Over time, changes within species lead to the replacement of old species by new species, as less successful species become
carly spends 9 hours a day working her job. what percentage of her day does she spend at work?