Calculus riddle: What do the Mean Value Theorem, the Washer and Shell Methods, and the Arc Length and Surface of Revolution formulas have in common? They all involve integration. Integration is very fancy addition. When you solve an integration problem, you take a weird shape whose area you can't directly determine, then you cut it up into tiny bits whose areas you *can* determine, and, finally, you add up all these little bits to determine the whole.