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integration is the area under each signal and it tells us the number of protons in that signal and so here we have the proton NMR spectrum of benzyl acetate including the integration values so the computer calculates the area under the signal so for example for this signal the area under the signals calculate by the computer and gives us this number the computer gives us 57.9 for this signal the computer gives us 23.1 and finally for this signal we get integration value of 35.4 let's go back up here to the dot structure of benzyl acetate and let's see how many protons that we need to account for in our proton NMR spectrum this carbon right here has three protons let me go ahead and draw those protons in alright this carbon has two protons on it and that's five so far and then on our ring right we have five more protons so going around the Ring here we have five more for a total of 10 so we need to account for 10 protons in our spectrum alright so going back to the integration values you find the smallest integration values so out of those three numbers twenty three point one is the smallest integration value and we're going to divide all three integration values by the smallest one and we'll start with 57.9 so fifty seven point nine divided by twenty three point one so let's get out the calculator here fifty seven point nine divide that by twenty three point one and we get two point five so I'll write two point five right here twenty three point one divided by twenty three point one is obviously equal to one and then finally thirty five point four we need to divide that by the smallest integration values so thirty five point four divided by twenty three point one gives us about one point five so we have one point five here and this gives us this gives us a ratio of the protons that are giving these three signals so the ratio would be two point five to one to one point five but you can't have two point five protons you can't have half a proton here and so those aren't the exact number of protons right we need to account for 10 protons in our molecule and so if you think about if you multiply these numbers by 2 alright then that gives us what we want because if you multiply 2.5 by 2 that gives us 5 if you multiply 1 by 2 that gives us 2 if you multiply 1 point 5 by 2 that gives us 3 and obviously 5 plus 2 plus 3 gives us 10 and 10 protons is how many protons that we need to account for for our molecule and so therefore therefore this signal right here corresponds to 5 protons this signal corresponds to 2 protons and this signal corresponds to 3 protons so if we go back up here to our dot structure and I look at these protons right so we have 3 equivalent protons the chemical shift for these protons we're next to a carbonyl so we would expect the chemical shift to be just past 2 and that's of course what we see right here so the shift is just past 2 this signal represents 3 protons and it's these 3 protons right here alright next let's look at these two protons so these 2 protons are next to an oxygen alright so the oxygen it DeShields that all those two protons protons are also next to this benzene ring over here so we would expect a higher chemical shift right and we have two protons and of course it's this signal which corresponds to two protons finally finally we have five nearly equivalent protons on our rings so there might not be exactly the same but for this signal here right we have we have five protons giving us this signal and it's a little bit more complex than the other ones but notice that notice where it is right we're in the aromatic region in terms of a chemical shift and so this signal must represent these five aromatic protons on our ring and so this shows you how how useful the integration values are they tell you they tell you how many protons are giving that signal which allows you to figure out the structure of the molecule