An issue with integrals involving absolute value

asked 2025-06-02 17:05:02 +0200

RL Pouso
31 ●1 ●2

updated 2025-06-02 21:44:39 +0200

slelievre
17809 ●22 ●163 ●352 http://carva.org/samue...

I have been using SageMathCell for a while and some things that used to work some months before seem to have changed and do not work any longer. In particular, I found the following problem when computing elementary integrals.

Can anyone explain me why "a" yields a correctly computed result but "b" is not computed at all? What should I do to get "b" correctly computed?

x, n = SR.var('x, n')
assume(n, 'integer')
a = integral(x^2*cos(n*x), x, -pi, pi)
b = integral(abs(x)*cos(n*x), x, -pi, pi)
print('a=', a)
print('b=', b)

edit retag flag offensive close merge delete

Comments

Welcome to Ask Sage. Thank you for your question.

slelievre ( 2025-06-02 21:45:05 +0200 )edit

I think the integration has some issues with absolute values. I forced my absolute value function, and the result is wrong:

def myabs(x):
    if x<0:
        return -x
    else:
        return x

x, n = SR.var('x, n')
assume(n, 'integer')
a = integral(x^2*cos(n*x), x, -pi, pi)
b = integral(abs(x)*cos(n*x), x, -pi, pi)
c = integral(myabs(x)*cos(n*x), x, -pi, pi)
print('a=', a)
print('b=', b)
print('c=', c)

a= 4*pi*(-1)^n/n^2
b= integrate(abs(x)*cos(n*x), x, -pi, pi)
c= 0

tolga ( 2025-06-04 08:22:33 +0200 )edit

add a comment

An issue with integrals involving absolute value

Comments

1 Answer

Your Answer

Question Tools

Stats

An issue with integrals involving absolute value edit

Comments

1 Answer

Your Answer

Question Tools

Stats

An issue with integrals involving absolute value