Let's represent the three consecutive even integers as x, x + 2, and x + 4 since even integers have a difference of 2 between them.
Now, we can set up an equation based on the information that their sum is equal to 84:
x + (x + 2) + (x + 4) = 84
Now, let's solve for x:
3x + 6 = 84
Subtract 6 from both sides:
3x = 84 - 6
3x = 78
Now, divide both sides by 3 to find the value of x:
x = 78 / 3
x = 26
So, the three consecutive even integers are 26, 28, and 30 because:
26 + 28 + 30 = 84