Methods in Calculus (Edexcel A-Level Further Mathematics): Flashcards

📚Flashcards
Improper Integrals
Sign up to keep revising.Create a free account to study more flashcards and track your progress.

Practise the cards

10 cards from this deck

Show

Two conditions making an integral improper

Integrand undefined OR range extends to infinity

Type I improper integral definition

Integrand undefined at one or more points

Type II improper integral definition

Range of integration extends to infinity

Evaluate af(x)dx\int_a^\infty f(x)dx using

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

Evaluate improper integral at discontinuity cc

limtc±atf(x)dx\lim_{t \to c^\pm} \int_a^t f(x)dx

Convergence condition: 11xpdx\int_1^\infty \frac{1}{x^p}dx

p>1p > 1

0ekxdx\int_0^\infty e^{-kx}dx for k>0k>0 equals

1k\frac{1}{k}

Limit notation: approaching 0 from positive side

0+0^+

11x2dx\int_1^\infty \frac{1}{x^2}dx

11

021xdx\int_0^2 \frac{1}{\sqrt{x}}dx

222\sqrt{2}

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

Explore Edexcel A-Level Further Mathematics Model Answers by Topics

Explore Edexcel A-Level Further Mathematics Quizzes by Topics

Explore Edexcel A-Level Further Mathematics Exam Questions by Topics

Join 100,000+ A-Level students studying Flashcards with us.

Select your subjects, and get access to A+ resources today.