Integration Using Completing the Square (College Board AP® Calculus AB)

Integration using completing the square

What is completing the square?

• Completing the square is a way of rewriting quadratic expressions

  • A quadratic expression is of the form

  • Rewriting can make them easier to use for various purposes

• The simple version of completing the square is

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    • E.g.

• When there is a coefficient in front of the this becomes

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    • E.g.

How can I integrate using completing the square?

• Recall the standard integrals

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  • See the 'Derivatives & Antiderivatives' study guide

• Completing the square can be used to get integrals into a form where these results can be used

  • The methods from the 'Integrals of Composite Functions' study guide may be needed as well

• E.g.

  • Complete the square on the denominator

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  • Rewrite the function to be integrated

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  • That is now a multiple of

    • This tells us that is going to be be our likely answer

  • To see if 'adjust and compensate' is needed, use the chain rule to differentiate

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  • Integrate

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