Improper Integrals (AQA A-Level Further Maths): Flashcards

Infinite limits or function undefined at/between limits

$\lim_{t \to \infty} \int_a^{t} f(x) dx$

Limit exists and equals a finite number

Limit doesn't exist or approaches infinity

BOTH parts must converge for original to converge

$0$ for any real $k$

$0$ for any real $k$

Two infinite limits or discontinuity between limits

Replace limit with variable, take limit from defined side

Divide by highest power of $x$ in denominator