The rectangular rules for numerical integration are illustred in Figure P2-15. The left side rule is despicted in Figure P2-15a, and the right side rule is despicted in Figure P2-15b. The integral of x(t) is approximated by the sum of the rectangular areas shown for each rule. Let y(kT) be the numerical integral x(t), 0<=t<=kT.

Write de difference equation relating y(k+1), y(k), and x(k) for the left side.

Write de difference equation relating y(k+1), y(k), and x(k+1) for the right side.

I know that the answers are:

a) For the left side:

y(k+1) = y(k) +Tx(k)

a) For the right side:

y(k+1) = y(k) +Tx(k+1)

I really don't understand clearly why is it. I'm reading about left and right side rules, but when it comes to do this exercise, I find it confused. Can anyone explain it to me in simple words?

LeftandRight.jpg

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