TITLE: How do you determine the complexity class of a problem like solving an integral?
QUESTION [5 upvotes]: The P and NP classes relate to decision problems, but what about calculus problems, specifically computing an integral? How does one figure out if a certain class of integrals is in P or NP? Can something like this be rephrased in terms of a decision problem? Or is there another, indirect method?

REPLY [2 votes]: You have to use a higher type model to faithfully talk about complexity and computability of operators in analysis like integration. You may want to check Akitoshi Kawamura's thesis "Computational Complexity in Analysis and Geometry". He proves that integration is $\mathsf{\#P\text{-}complete}$ operator.