Jump to content


Photo
- - - - -

Algebra


  • Please log in to reply
3 replies to this topic

#1 BenildoAlexandre

BenildoAlexandre

    Curious

  • Members
  • Pip
  • 3 posts

Posted 31 May 2015 - 07:50 PM

guys i have a doubt.

i want to integrate from -2pi to -pi and then from -pi to zero but i am not sure about the expression of the ramp decreassing from 4 to zero on the y axis and from -2pi to -pi.

from -pi to 0 i would just integrate the amplitude of 2 of the function.

 

regards

 



#2 CraigD

CraigD

    Creating

  • Administrators
  • 8034 posts

Posted 01 June 2015 - 10:10 PM

I think you’re trying to find
[math]\int_{-2 \pi}^{2 \pi} \left( -\frac1{2 \pi}x +2 \right) dx[/math]

which, involving a simple polynomial, is easy to find:
[math] -\frac1{2 \pi} x^2 +2x |_{-2 \pi}^{2 \pi}[/math]

[math] = \left( -\frac1{2 \pi} (2 \pi)^2 +2(2 \pi) \right) - \left( -\frac1{2 \pi} (-2 \pi)^2 +2(-2 \pi) \right) = 8 \pi [/math]

You could just do this geometrically by noting that the graph of [math]-\frac1{2 \pi}x +2[/math] is
Attached File  Capture.PNG   3.95KB   0 downloads
And finding the area of the right triangle with sides [math]4 \pi[/math] and [math]4[/math].
  • Buffy likes this

#3 sanctus

sanctus

    Resident Diabolist

  • Administrators
  • 4225 posts

Posted 02 June 2015 - 01:24 AM

CraigD, very impressed that you got the integrand from the opening post!!



#4 BenildoAlexandre

BenildoAlexandre

    Curious

  • Members
  • Pip
  • 3 posts

Posted 05 June 2015 - 05:21 AM

i wanted to integrate just the decreasing ramp from -2pi to -pi.....i computed the line equation for slope............thanks  guys