Integrating x(1-x)^1/2: A Calculus Headache Solved

Click For Summary

Homework Help Overview

The discussion revolves around evaluating the integral ∫ x(1-x)^(1/2), a problem situated within the calculus subject area. Participants express frustration over discrepancies between their results and those found in a textbook.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using substitution methods to simplify the integral, with one participant attempting to express the integral in terms of a new variable. There are questions about how to factor terms and achieve the form presented in the textbook.

Discussion Status

Some participants have offered insights into potential factoring techniques, while others are still grappling with the integration process. There is a sense of progress as one participant believes they have resolved their confusion, although no consensus has been reached on the correct approach.

Contextual Notes

Participants mention a specific textbook solution that differs from their own calculations, indicating a potential misunderstanding or misalignment in the integration process. There is also a sense of urgency and frustration expressed regarding the complexity of the problem.

Jbreezy
Messages
582
Reaction score
0

Homework Statement



Hey I'm doing something really stupid it is really pissing me off why I can't figure it out.




The Attempt at a Solution



Evaulate the integral : ∫ x(1-x)^1/2

I tried with substitution. u = 1-x , -du = dx and x = 1-u

∫ (1-u)(u)^1/2 I just tried to simplify it some.

∫ (u^1/2-u^3/2) -du

-∫ u^1/2 du +∫ u^3/2 du

integrate I got

(-2/3)u^ 3/2 + (2/5)u^5/2


(-2/3)(1-x)^ 3/2 + (2/5)(1-x)^5/2


My book got (-2/15)*2+3x)(1-x)^3/2 + C
I'm lost.

Thanks for the help.
 
Physics news on Phys.org
Jbreezy said:

Homework Statement



Hey I'm doing something really stupid it is really pissing me off why I can't figure it out.




The Attempt at a Solution



Evaulate the integral : ∫ x(1-x)^1/2

I tried with substitution. u = 1-x , -du = dx and x = 1-u

∫ (1-u)(u)^1/2 I just tried to simplify it some.

∫ (u^1/2-u^3/2) -du

-∫ u^1/2 du +∫ u^3/2 du

integrate I got

(-2/3)u^ 3/2 + (2/5)u^5/2


(-2/3)(1-x)^ 3/2 + (2/5)(1-x)^5/2


My book got (-2/15)*2+3x)(1-x)^3/2 + C
I'm lost.

Thanks for the help.

It looks to me like they factored (1 - x)3/2 from both terms.
 
I just tried that and couldn't get it in the form they had.
 
I think I just got it sorry. Jesus this was mad so much harder by me ..Thanks for help
 

Similar threads

Replies
3
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 27 ·
Replies
27
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K