Question

Consider the function f(x) = 5/x^4 - 8/x^8, let F(x) be the anti derivative of f(x) with F(1) = 0. Then F(4) =?

Answer 1

haven't done much on that
amistre64 or maybe Hero would though

Answer 2

what does "anti derivative" mean?

Answer 3

It means F(x) ' = f(x) , right?

Answer 4

yeah except its f'(x) = f(x)

Answer 5

nope, F'(x) = f(x)
not f'(x) = f(x)
f'(x) =f(x) if and only if f(x) = e^x

Answer 6

oh yeah your right

Answer 7

Now, find F(x)
you have f(x) = \(5x^{-4}-8x^{-8}\)
do the first term first. \((something)'= 5x^{-4}\), can you find that "something"
Or, do you study integral yet?

Answer 8

we've studied integrals

Answer 9

oh, it is wwwwwwwwwway easier, just take integral of f(x) , you get F(x)

Answer 10

would it be -5/3(x)^-3

Answer 11

do both them at the same time since you are allowed using integral. :)

Answer 12

and then theres 8/7(x)^-7

Answer 13

right?

Answer 14

yes

Answer 15

and +C

Answer 16

right so then i find C?

Answer 17

yep

Answer 18

im not sure if its right, i got -59/21, can you check it?

Answer 19

nope

Answer 20

you substitute 1 for x and equal it to 0 right?

Answer 21

\(F(x) = \dfrac{-5}{3}x^{-3}+\dfrac{8}{7}x^{-7}+C\)

Answer 22

now F(1) = 0
that is \(C= \dfrac{5}{3}-\dfrac{8}{7}=\dfrac{35-24}{21}=\dfrac{11}{21}\)

Answer 23

I think you mess up at the second term .
Integral of \(-8x^{-8} \) is 8/7 x^(-7)

Answer 24

i did get that

Answer 25

how about C? To me, I isolate C first, then replace x =1 to find C and it is 11/21 as shown

Answer 26

yeah i get that

Answer 27

Good, then just plug that C into F(x) to find F(4)

Answer 28

ok thnx, lets see wat i get?

Answer 29

ok i got the answer, thnx for ur help @Loser66

Answer 30

yw