Expii

# Computing Improper Integrals with an Undefined Endpoint - Expii

An improper integral with a single infinite singularity at an endpoint $$c$$, like $$\int_a^c f(x)\,dx$$ or $$\int_c^b f(x)\,dx$$, can be interpreted as a single limit of definite integrals, as long as the interval (namely, $$[a,c]$$ or $$[c,b]$$) is bounded. Specifically, $$\int_a^c f(x)\,dx$$ is defined as $$\lim_{t\to c^-} \int_a^t f(x)\,dx$$, while $$\int_{c}^b f(x)\,dx$$ is defined as $$\lim_{t\to c^+} \int_t^b f(x)\,dx$$.