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were gonna take a look at evaluating definite integrals geometrically and this is not a new topic for us however in particularly were gonna look at what to do when you have been given an initial condition so lets take a look at this first problem weve been given the graph of G prime of X so we know that we have the graph of a derivative weve been told that G of 5 is 12 which means that on the original function we know that the point five twelve exists set up and evaluate an integral expression to find the following so the first thing that we want to find is G of eight we want to find the value of the original function when youre doing that however youve got to consider that you have been given this initial condition so think of it like this when were going to find or evaluate a definite integral and thats what were going to do were going to use the definite integral because over here we have the graph of G prime of X thats our only connection to getting back to the original