My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 24th, 2013, 12:58 AM   #1
Senior Member
 
Joined: Oct 2012

Posts: 460
Thanks: 0

int x^2sin2x dx

I am given to evaluate:



Please, the result is 1/4...I can't get this...should it be just normal multiplying rule for integrals or something else?

Many thanks!
ungeheuer is offline  
 
January 24th, 2013, 01:06 AM   #2
Math Team
 
Joined: Apr 2010

Posts: 2,276
Thanks: 220

Re: int x^2sin2x dx

Can you do it using integration by parts? It was shown to you here.
Hoempa is offline  
January 24th, 2013, 02:19 AM   #3
Senior Member
 
Joined: Oct 2012

Posts: 460
Thanks: 0

Re: int x^2sin2x dx

Hello!
The problem is:

dv= sin2x

how do we get v then?

so we search what would give us derivative =sin2x, am I right?
so sin2x is derivative of v
And that is problem!
Many thanks!
ungeheuer is offline  
January 24th, 2013, 02:25 AM   #4
Math Team
 
Joined: Apr 2010

Posts: 2,276
Thanks: 220

Re: int x^2sin2x dx

One way is to use [-cos(a)]' = sin(a) * [a]'.
Sub 2x = a in your equation.

Another is use so
Hoempa is offline  
January 24th, 2013, 06:46 AM   #5
Senior Member
 
Joined: Oct 2012

Posts: 460
Thanks: 0

Re: int x^2sin2x dx

Hello!
so:





so:


[latex]=(-\frac{x^2}{2}cosx-\int((-cosx)[latex]
we should get:


Can someone help?
Many thanks!!!
ungeheuer is offline  
January 24th, 2013, 07:57 AM   #6
Math Team
 
Joined: Apr 2010

Posts: 2,276
Thanks: 220

Re: int x^2sin2x dx

u = x^2 yields du = 2x dx instead of 2. Can you get it from here?
Hoempa is offline  
January 24th, 2013, 08:08 AM   #7
Senior Member
 
Joined: Oct 2012

Posts: 460
Thanks: 0

Re: int x^2sin2x dx

[color=#0000FF]Huh!








but the result is up there... not that...please, where is the mistake?





[/color]
ungeheuer is offline  
January 24th, 2013, 08:28 AM   #8
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 2,962
Thanks: 239

Re: int x^2sin2x dx

Hello, ungeheuer!

Quote:


Please, the result is 1/4[color=beige] . [/color][color=blue]How?[/color]

Integrate by parts:

[color=beige]. . [/color]




By parts again:

[color=beige]. . [/color]





soroban is offline  
January 24th, 2013, 09:15 AM   #9
Senior Member
 
Joined: Oct 2012

Posts: 460
Thanks: 0

Re: int x^2sin2x dx

[b]Many thanks, soroban!
All clear now!!!
ungeheuer is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
int, x2sin2x



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes






Copyright © 2014 My Math Forum. All rights reserved.