Algebra

[BenildoAlexandre]

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

 

[CraigD]

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

And finding the area of the right triangle with sides [math]4 \pi[/math] and [math]4[/math].

[sanctus]

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

[BenildoAlexandre]

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