In this case can I break the mod value and write like this
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In this case can I break the mod value and write like this
No. On the interval [2,1) x+1 = x1, while on the interval [1,2], x+1 = x+1. So what you WANT is:
Hello, srirahulan!
Quote:
Code:
 .*
 .*.:
 .*...:
 .*.....:
 .*.......:
.*.........:
*. .*...........:
:.*. .*............:
:...*. .*..............:
+*+++
2 1  1 2

Notice that, per Soroban's graph, this can be done with any "integration". The answer is the sum of the areas of two triangles.
Indeed...using just "plain geometry" (ok, a lame pun), it is apparent that the integral:
, while:
.
The reason being, the triangle with base extending from (2,0) to (1,0) in the former integral has a "peak" at (2,1) and lies BELOW the xaxis (so has "negative area", that is the integral is negative in this region), while in the latter integral lies above the xaxis (with "peak" at (2,1)). This triangular area has a base of 1, and a height of 1, and so has area 1/2, making a "swing" of a difference of 1 between the two integrals.
And yes, Halls, that WAS a typo. :P