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Not an answer:

In SMC, I'm running into the error that the question mentions. I'm not certain of the current version of Sage that SMC is using.

The following command produces the error:

integrate(sin(pi*k*t/2),t,0,1)

However, the next two commands do not.

integrate(sin(k*t/2),t,0,1)
integrate(sin(pi*k*t/2. ),t,0,1)

This seems quite odd. Any ideas?

Not an answer:

In SMC, I'm running into the error that the question mentions. I'm not certain of the current version of Sage that SMC is using.

The following command produces the error:

integrate(sin(pi*k*t/2),t,0,1)

However, the next two commands do not.

integrate(sin(k*t/2),t,0,1)
integrate(sin(pi*k*t/2. ),t,0,1)

This seems quite odd. Any ideas?For more oddness, I found that integrate(sin(pi*k1*t/2),t,0,1) works just fine if k1 is defined as a variable. According to the other answer, the original integral works in 7.1. So, there must have been an odd error in version 6.10. My advice is to switch your code to have k1 rather than k. I tried this with your code, and it worked.