--> integration
« previous next »
Pages: [1]   Go Down

Author Topic: integration  (Read 1071 times)

Offline Light

  • SF Immigrant
  • **
  • Posts: 51
  • Reputation: 355
integration
« on: February 06, 2010, 02:01:33 pm »
how to integrate by recognition: (7x^2)(x^3 +1)^5 dx ?
Logged

Offline astarmathsandphysics

  • SF Overlord
  • *********
  • Posts: 11271
  • Reputation: 65534
  • Gender: Male
  • Free the exam papers!
Re: integration
« Reply #1 on: February 06, 2010, 02:22:47 pm »
Multiply the bracket out then integrate term by term using \int Ax^n dx = \frac{Ax^{n+1}}{n+1}
« Last Edit: February 06, 2010, 02:24:30 pm by astarmathsandphysics »
Logged

Offline Light

  • SF Immigrant
  • **
  • Posts: 51
  • Reputation: 355
Re: integration
« Reply #2 on: February 06, 2010, 02:30:02 pm »
but the answer is in form of factorised with power.is there any shorter way?power 5 need long way of expanding.==
Logged

Offline astarmathsandphysics

  • SF Overlord
  • *********
  • Posts: 11271
  • Reputation: 65534
  • Gender: Male
  • Free the exam papers!
Re: integration
« Reply #3 on: February 06, 2010, 02:34:49 pm »
I didn't see the power cos I was blinded by q80's link. Better then integration by substition

u=x^3+1
u=x^3 so du=3x^2 dx
\int 7x^2(x^3+1)^5dx=\int 7/3 u*u^5du=\int 7/3 u^6du = 7/18 u^6 =7/18 (x^3+1)^6 +C
« Last Edit: February 06, 2010, 03:01:37 pm by astarmathsandphysics »
Logged

Offline Light

  • SF Immigrant
  • **
  • Posts: 51
  • Reputation: 355
Re: integration
« Reply #4 on: February 06, 2010, 02:35:48 pm »
but question says integration  by recognition.
Logged

Offline astarmathsandphysics

  • SF Overlord
  • *********
  • Posts: 11271
  • Reputation: 65534
  • Gender: Male
  • Free the exam papers!
Re: integration
« Reply #5 on: February 06, 2010, 03:02:33 pm »
I am surprised. Manipulation involved. See my answer above
Logged
Pages: [1]   Go Up
« previous next »
 

\n\t\t\t\t\t\t\t\t\t
<' + '/div>\n\t\t\t\t\t\t\t\t\t