Tips For How To Understand Application of Integrals In Physics Volume integrals are where the real trouble starts If you know you have to take the integral of something in 3-dimensional space, you could start having problems A lot of problems typically do have you integrate towards infinity which in cartesian is coordinates is pretty easy
Swapping Integrals and Sums: When is it Justifiable? - Physics Forums No, the sums in joshmccraney's post are infinite sums, so you cannot guarantee that exchanging the integrals and sums is valid Usually the infinite sum needs to be uniformly convergent to swap the sum and integral
Are there mathematicians that dislike integral calculus? - Physics Forums Solving integrals by hand is difficult and prone to errors, and the techniques such as integration by parts, partial fraction decomposition, and trig substitutions only work for a small subset of integrals and I do not see the point of avoiding technology like Wolfram Mathematica for mathematical research
I Feel Weird Using Integral Tables - Physics Forums Sorry if this is in the wrong place Sometimes I do really stupid things on integrals (use a method that gets me nowhere, make a mistake while factoring quickly, etc ) I have always been reluctant on using tables because I always felt stupid using them I feel like I have to reinvent every
Fourth Integral: What is the Answer? - Physics Forums Double and triple integrals do not necessarily represent areas and volumes, you can compute both area and volume (in some special cases) with a single integral! In your analogy though, an n-dimensional integral generally represents and n-dimensional volume, of which 2 is area and 3 our 'classic' volume