In a simple case, subtracting indefinite integrals works just fine.Ĭonsider computing the area under a sine curve, which equals And to get the correct answer one needs to be considerably more sophisticated. The answer, as is often the case, is that in the real world of mathematical computation, things are more complicated than one learns in basic mathematics courses. So how come inside Mathematica there are thousands of pages of code devoted to working out definite integrals-beyond just subtracting indefinite ones? After all, they might think, the fundamental theorem of calculus says that one just has to subtract the values of the indefinite integral at the end points to get the definite integral. Most calculus students might think that if one could compute indefinite integrals, it would always be easy to compute definite ones.
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