Algebra

3 replies to this topic

#1 BenildoAlexandre

BenildoAlexandre

Curious

• Members
• 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

• 8034 posts

Posted 01 June 2015 - 10:10 PM

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

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

$= \left( -\frac1{2 \pi} (2 \pi)^2 +2(2 \pi) \right) - \left( -\frac1{2 \pi} (-2 \pi)^2 +2(-2 \pi) \right) = 8 \pi$

You could just do this geometrically by noting that the graph of $-\frac1{2 \pi}x +2$ is
And finding the area of the right triangle with sides $4 \pi$ and $4$.
• Buffy likes this

#3 sanctus

sanctus

Resident Diabolist

• 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
• 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