Question

HELP PLEASE!!!

Answer 1

\[\int\limits_{x}^{x^4}t^4dt\]

Answer 2

ok, so where are you confused at?

Answer 3

I thought it would be (x^20-x^5)/5, but it says it isn't right

Answer 4

so, let's see. You got 1/5 t^5 then plugged in

Answer 5

yeah

Answer 6

hm, do you think they wanted you to factor out the x^5? (I agree with your answer. So long as how you typed it here is the same as the site)

Answer 7

oh, maybe parentheses around the 20?

Answer 8

I have tried that too, but still wasn't right

Answer 9

hmm. Can you post the question as written?

Answer 10

that is how it is written. It is looking for f'(x)

Answer 11

hmm. Well we are assuming x is positive to have that be the answer.

Answer 12

I mean this is straight FTC

Answer 13

Like I don't understand at all what's wrong

Answer 14

Give me a sec to double check myself.

Answer 15

ok

Answer 16

Oh, that x^4 we forgot to apply the chain rule

Answer 17

ok, so we swap in x^4 for everything, but we need to replace dt with the derivative of x^4

Answer 18

and does it ask for f ' (x)?

Answer 19

Is it asking for the derivative?

Answer 20

yeah

Answer 21

You found the integral, not the derivative.

Answer 22

now, I got what happened

Answer 23

ok, so, you need to first (in your work that is) break up the integral into two integrals will some constant for the other limit

Answer 24

then, it's a plug and chug, for subbing into dt you take the derivative of your functions. With x, it's just 1, but for x^4, as you know, it changes things

Answer 25

Do you want to try it, or would you like me to find you a link or video that explains it better first?

Answer 26

so you find the derivative then plug it in?

Answer 27

sort of.

Answer 28

you are finding the derivative of an integral

Answer 29

they are inverse functions, so, they cancel each other out

Answer 30

i'm not following what you are saying

Answer 31

so, here, watch this video (or the series) and I can take you through it. I'm botching explaining it. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwjQ7a70k_bKAhVGOj4KHZ8WBmYQtwIIHTAA&url=https%3A%2F%2Fwww.khanacademy.org%2Fmath%2Fintegral-calculus%2Findefinite-definite-integrals%2Ffundamental-theorem-of-calculus%2Fv%2Fboth-bounds-being-a-function-of-x&usg=AFQjCNHda_m7wFPkPLG-OR_Q-pdOVS4J1Q

Answer 32

I can take you through after you watch it, but essentially, the Fundamental theorem of calc and inverse functions are what's taking place

Answer 33

Alright I got it thank you for the help. I see what I was doing wrong

Answer 34

np, sorry I couldn't explain it more concisely

Answer 35

First, please include the instructions for this problem. You've posted only an integral, without instructions.

Look up "derivative of a function expressed as an integral."

Whatever you do, don't forget that you MUST use the Chain Rule twice here.