integration
An NMR spectrum tells you where each kind of hydrogen lives through chemical shift, but it also answers a wonderfully practical question: how many of each kind are there? The answer is hidden in the size of each signal. Integration is the measurement of the area under each peak, and that area is directly proportional to the number of hydrogens producing it. A signal twice as large means twice as many hydrogens.
Crucially, integration gives ratios, not absolute counts. The instrument draws a stepped line (the integral trace) or prints numbers over each peak, and what matters is the ratio between them. If three signals integrate to 3 : 2 : 1, you know the hydrogens come in that proportion — but the molecule could have 3 : 2 : 1 actual hydrogens, or 6 : 4 : 2, and so on. You pin down the absolute numbers by combining the ratio with the total hydrogen count from the molecular formula. If the formula says ten hydrogens and the ratio is 3 : 2 : 5, then the groups have 3, 2, and 5 hydrogens.
Integration is the clue that turns a row of peaks into a real count of CH3, CH2, and CH groups. A 3-hydrogen signal usually means a methyl group; a 2-hydrogen signal often a CH2; a single large 5-hydrogen signal in the aromatic region whispers a monosubstituted benzene ring (C6H5-). Combined with chemical shift and splitting, integration is one of the four pillars that let a chemist rebuild the full carbon-hydrogen framework.
In ethyl acetate (CH3-CO-O-CH2-CH3), the three signals integrate in a 3 : 2 : 3 ratio — the acetyl CH3, the OCH2, and the ethyl CH3 — matching the eight hydrogens of the formula directly.
Integration gives the ratio of hydrogens; combine with the formula for absolute counts.
Integration is reliable for 1H NMR but ordinary carbon-13 NMR is usually not integrated quantitatively — relaxation differences make 13C peak areas an unreliable count of carbons, so do not read carbon spectra the same way.