Computing Multi-Step Improper Integrals
Read this topicExplanations 2
- A general method to approach improper integrals: For how many reasons is it improper? Break it up into several improper integrals until a) each improper integral is only imprope…
By Panavia Shou, Alex Federspiel
- Overview of "multi-step" improper integrals We now understand two-step improper integrals: those that can be broken into two one-step improper integrals. In general, an improper…
By Victor Wang
Problems 3
- If f(x)f(x)f(x) goes to infinity at exactly four finite xxx-values, how many integrals would you need to split ∫−∞∞f(x) dx\int_{-\infty}^\infty f(x) \,\text{d}x∫−∞∞f(x)dx into?
- If f(x)f(x)f(x) has an infinite number of singularities (i.e. goes to infinity at infinitely many xxx-values), is it still possible for ∫−∞∞f(x) dx\int_{-\infty}^\infty f(x) \, …
- Define a function fff as follows: For every integer kkk, f(k)=0f(k) = 0f(k)=0. For all x∈(k,k+1)x \in (k, k+1)x∈(k,k+1), f(x)={2−k(x−k)if k is even2−k−(x−k−1)if k is oddf(x) = \…