improper-integrals

Improper integrals

What are improper integrals?

• An improper integral is a definite integral where one or both of the limits is either:

  • Positive or minus infinity

  • A point where the function is undefined

    • Consider the graph of 

    • It is undefined at the point x = 0

    • The integral of with a limit of zero would be an improper integral

• Examples include:

  • 

  • <img alt=”integral subscript 1 superscript infinity 1 over x cubed d x equals limit as b rightwards arrow infinity of integral subscript 1 superscript b 1 over x cubed d x” data-mathml='<math ><semantics><mrow><msubsup><mo>∫</mo><mn>1</mn><mo>∞</mo></msubsup><mfrac><mn>1</mn><msup><mi>x</mi><mn>3</mn></msup></mfrac><mo>d</mo><mi>x</mi><mo>=</mo><munder><mi>lim</mi><mrow><mi>b</mi><mo>→</mo><mo>∞</mo></mrow></munder><msubsup><mo>∫</mo><mn>1</mn><mi>b</mi></msubsup><mfrac><mn>1</mn><msup><mi>x</mi><mn>3</mn></msup></mfrac><mo>d</mo><mi>x</mi></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″}</annotation></semantics></math>’ height=”52″ role=”math” 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