In most states, the capital of the state is NOT the biggest city in the state.
Using a data set from the US Geological Service that includes location and 2010 Census population data, we made a map showing every state's capital and largest city. States where the capital is the largest city are in green, and their capitals are in yellow. States where the capital is not the largest city are in grey, and their capitals are in red and largest cities in blue:
Here's the list of states where the capital is the largest city:
And the states where the capital is not the largest city: