# integration

Discussion in 'Homework Help' started by GMChandio, Apr 27, 2015.

1. ### GMChandio Thread Starter New Member

Feb 26, 2015
28
0
Question 2, i tried to do it but couldn't.

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2. ### Papabravo Expert

Feb 24, 2006
10,148
1,791
In your first attempt you are doing things which are not allowed.

$(x-x^3)^{\frac13}\quad \ne \quad x^{\frac13}-x$

Last edited: Apr 27, 2015
3. ### GMChandio Thread Starter New Member

Feb 26, 2015
28
0
How can i solve further without simplifying?
Besides i only know this method to solve problems, simplify and apply the formula.

4. ### WBahn Moderator

Mar 31, 2012
17,757
4,800
Your very first step shows that you have a fundamental weakness in your algebra skills. You start of by asserting that

$
{$$x-x^3$$}^{\frac{1}{3}} \, = \, x^{\frac{1}{3}}-x
$

By this line of reasoning,

$
{$$a+b)}^{2} \, = \, a^2 + b^2 $ Do you agree with this? If you do, then just set a=b=1 and see if it actually works out. 5. ### WBahn Moderator Mar 31, 2012 17,757 4,800 What method? 6. ### GMChandio Thread Starter New Member Feb 26, 2015 28 0 No i don't agree with that (a+b)²= a²+2ab+b² 7. ### GMChandio Thread Starter New Member Feb 26, 2015 28 0 Then can you tell me or give me a link of how to solve such problems? 8. ### WBahn Moderator Mar 31, 2012 17,757 4,800 One route you can go is to just differentiate the possible answers and see which one yields the original integrand. I would do the one that has "+1+C" last since the 1 could be absorbed into the C which means that this answer is probably a distractor. 9. ### Papabravo Expert Feb 24, 2006 10,148 1,791 So that simplification will not work. You'll have to find another one. As an aid to figuring this out did it occur to you to differentiate one or more of the answers? Also if you can get the integral into the form $\int u\cdot du$ then maybe you can solve it. Last edited: Apr 27, 2015 10. ### GMChandio Thread Starter New Member Feb 26, 2015 28 0 That would take a lot of time, differentiating all the options 11. ### GMChandio Thread Starter New Member Feb 26, 2015 28 0 Like what? Give me some hint or something iam not asking for complete solution 12. ### GMChandio Thread Starter New Member Feb 26, 2015 28 0 That would take a lot of time, differentiating all the options 13. ### GMChandio Thread Starter New Member Feb 26, 2015 28 0 Differentiating all the options ia going to take alot of time, and iam going to get just over a minute to solve this kind of queation, i've got a test coming up in no time. 14. ### WBahn Moderator Mar 31, 2012 17,757 4,800 Really? I did it in less than three minutes. Look at the three options -- they all have the same primary component, namely $ {\( \frac{1}{x^2} - 1$$}^{\frac{4}{3}}
$

How hard can it be?

15. ### Papabravo Expert

Feb 24, 2006
10,148
1,791
Which is worse
1. Taking a bit of time
2. Passing on answering the question

16. ### GMChandio Thread Starter New Member

Feb 26, 2015
28
0
It maybe easy for you.
But the answer is C, not A.

17. ### GMChandio Thread Starter New Member

Feb 26, 2015
28
0
If i wanted to pass this question, i wouldn't have wasted half an hour tring to solve it.

18. ### Papabravo Expert

Feb 24, 2006
10,148
1,791
OK, it's completely up to you how you approach your problems.

19. ### WBahn Moderator

Mar 31, 2012
17,757
4,800
Yes, the answer is C. Where did I, or anyone, say that the answer is A?

I said that all three of the possible answers could be evaluated by differentiating that one expression.

20. ### WBahn Moderator

Mar 31, 2012
17,757
4,800
Let me walk you through it one step at a time.

What is

$
\frac{d}{dx}${$$\frac{1}{x^2} - 1$$}^{\frac{4}{3}}$
$

I picked this form instead of the (1 - 1/x^2) form simply because this is the form used in two of the three potential answers. But hopefully you recognize that the differ only by a minus sign.