How do you evaluate the integral of cscx dx between the interval [pi/2,pi]?


To find the integral of ##intcscxdx## between [##pi/2##,##pi##], use this theorem :
##intcscx## = Ln ##abs(cscx+cotx)##+c

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when written in proper notation it should look like this:
##[Ln(abs(cscx+cotx) )]_(pi/2)^(pi)##

to evaulate, you must plug in both upper and lower limits to the antiderivative then subtract the lower limit from the upper limit.

However, ##csc(pi)## does not exist. On the graph below, the region from ##csc(pi/2)## onwards goes to infinity because there is no upper bound, so the answer to the integral is ##+oo##.
graph{cscx [-1.47, 6.324, -0.558, 3.338]}

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