U-Substitution in Calculus: Solving a Difficult Integration Problem

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Homework Help Overview

The problem involves evaluating the integral of (x^7)/sqrt(4-3x^16) from 0 to 1, with a focus on applying u-substitution in calculus.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the necessity of finding an appropriate u for substitution that would yield the term x^7 in the differential du. There are attempts to identify suitable substitutions, with some questioning the reasoning behind their choices.

Discussion Status

The discussion is ongoing, with some participants providing hints and guidance regarding the u-substitution process. There is a recognition of the original poster's struggles with calculus concepts, and suggestions to seek additional help from a teacher have been made.

Contextual Notes

Participants note the original poster's limited understanding of calculus, particularly in relation to integration and substitution techniques. There is an acknowledgment of the need for further clarification and support.

javacola
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Homework Statement


1~~0 (x^7)/sqrt(4-3x^16) dx




The Attempt at a Solution



There really isn't one. I am as clueless as one can get in calculus. I know that I am supposed to substitute the variable "u" in for a section of this problem, but really don't know anything after that. I understand derivatives but that is about it. If someone could walk me through this problem it'd be great.
 
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javacola said:

Homework Statement


1~~0 (x^7)/sqrt(4-3x^16) dx

The Attempt at a Solution



There really isn't one. I am as clueless as one can get in calculus. I know that I am supposed to substitute the variable "u" in for a section of this problem, but really don't know anything after that. I understand derivatives but that is about it. If someone could walk me through this problem it'd be great.

You know that when you make a u substitution, you need the du to be in the integral. You have x7 sitting there. What u might give you an x7 in the du? Think about that.
 
LCKurtz said:
You know that when you make a u substitution, you need the du to be in the integral. You have x7 sitting there. What u might give you an x7 in the du? Think about that.

7x^6?
 
LCKurtz said:
You know that when you make a u substitution, you need the du to be in the integral. You have x7 sitting there. What u might give you an x7 in the du? Think about that.

javacola said:
7x^6?

No, you are just guessing. If you want to get x7 in the answer for du, what must u be? You got x6 in your answer, not x7. C'mon, you can do better than that.
 
Last edited:
LCKurtz said:
No, you are just guessing. If you want to get x7 in the answer for du, what must u be? You got x6 in your answer, not x7. C'mon, you can do better than that.

I told you I don't know much about calculus...so just saying "come on" isn't going to magically help me get the answer.

Is u x^7? Or 4-3x^16?
 
If you honestly have no idea what to do, even with LCKurtz's very good hint, there isn't a lot we can do for you. You really need to talk to your teacher about this kind of problem.
 

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