How did the change occur indicated by the red arrow? please explain in regards t

Question

How did the change occur indicated by the red arrow?

please explain in regards to the max(x,r) how this disappeared and also how the integration upper/lower limits changed.

thank you!

Explanation / Answer

here max(x,r) is a function whose output is either r (if r>x ) or x if(x>r) so max (x,r) = r for r between 0 to r but (because in this interval r is greater x) and after x= r.... "x" becomes greater than r so the interval has been splitted into two part one from 0 to r and next from r to infinity,...... for example say r = 9 so on the number line from x= 0 to 9 its r(which is equal to 9) which is greater than 9 but after x = 9 its x which now becomes greater than r(which is still = 9)...... so max(9.x) = 9 for x9..... hope this helps

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