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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

How to do this integral?

I used an u-substitution and then integration by parts and I got -5/4

This was in a timed quiz so I had hurry and im not sure I got it right? Is my answer correct? If not, how do you do it then?

Last edited by LuisRodg (2008-02-18 05:19:24)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: How to do this integral?

I haven't done this yet, so don't take my word for anything, but wouldn't the answer have to be positive, as the whole curve (and so the section of the curve between 0 and 1) is above the x-axis?

Last edited by Daniel123 (2008-02-18 05:30:28)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: How to do this integral?

One of the dangerous things with integration by parts is forgetting that dang negative sign.  I got that it's 1/4.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

dchilow

Member

Registered: 2007-03-05

Posts: 27

Re: How to do this integral?

Can't you just plug it into the 89?

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: How to do this integral?

Not allowed any form of calculator in quizzes or tests. Makes sense though. I want to learn how to do it myself not plug it in some calculator.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: How to do this integral?

This is just from a few minutes of scribbling, but I got it as ln(2) - 1/4.
I'll double-check later.

Edit: Wait, I get 1/4 after all. I did exactly what Ricky warned about. >_>

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Why did the vector cross the road?
It wanted to be normal.

Krizalid

Member

Registered: 2007-03-09

Posts: 51

Re: How to do this integral?

Let's perform a double integration solution:

The rest follows. Easy, huh ¿?

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: How to do this integral?

I do not follow that approach since I havent been introduced to double integrals yet.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: How to do this integral?

lol! has everyone gone nuts? Double integrals?

Let u = ln(x + 1)

let dv = x dx

its easy as pi!

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A logarithm is just a misspelled algorithm.

saudi_boy

Member

Registered: 2006-11-01

Posts: 41

Re: How to do this integral?

yes the final solution , in my opinion, 1/4

you need to use integration by parts

lol! has everyone gone nuts? Double integrals?

Let u = ln(x + 1)

let dv = x dx

its easy as pi!

then use substitution with (x+1)=u   in second term of integral   ( du*v)

if you don't understand yet

i can help you more

tell me my brother if you get

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: How to do this integral?

And now for the new integral?

Last edited by LuisRodg (2008-03-30 13:41:08)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: How to do this integral?

There are two ways you could do the new integral:

1. Use the substitution u = x + 1

2. Use long division twice, leaving you with three terms that are easy to integrate (much nicer )

Last edited by Daniel123 (2008-03-30 22:57:09)

mleiner

Member

Registered: 2008-04-02

Posts: 2

Re: How to do this integral?

after long division it becomes
(1/2)x^2(ln(x+1)) - (1/2)[∫x-1 dx + ∫(1/(x+1)) dx