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The Integral: the Anti-derivative

The Integral: the Anti-derivative. By: Ashley Wang Math Analysis Honors: Period 4 November 2007. First Step. Simplify, if possible. This will make things a lot easier. ∫ (7x+2x+3) 8 ∫ (9x+3) 8. Second Step. Make your guess.

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The Integral: the Anti-derivative

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  1. The Integral: the Anti-derivative By: Ashley Wang Math Analysis Honors: Period 4 November 2007

  2. First Step • Simplify, if possible. • This will make things a lot easier. • ∫ (7x+2x+3)8 • ∫ (9x+3)8

  3. Second Step • Make your guess. • Raise the exponent– of the entire problem– to one number higher. • G:  (9x+3)9

  4. Third Step • Check your work. • Do this by setting the derivative of your guess equal to the original problem. • C: 9 (9x+3)8 * (9) = (9x+3)8 • =1/81 • HINT: Remember the package rule!

  5. Fourth Step • Plug the  into the guess to get the final answer. • 1/81  (9x+3)9  1/81 (9x+3)9 • A: 1/81 (9x+3)9 • THIS is the integral of the problem.

  6. Fifth Step • You could always double-check the answer, just to be absolutely sure. • It doesn’t hurt! • So, just take the derivative of the final answer and see if it equals the original problem. • If not, go back and check your work.

  7. Fifth Step continued… • A: 1/81 (9x+3)9 • A’: 9 * 1/81 * (9x+3)8 * (9) •  (1/9) * (9) * (9x+3)8 •  (9x+3)8 • Yup, the answer is perfecto!

  8. THE END • Thank you Mr. Wiencek for watching my presentation and… • THANK YOU in advance, for giving me an ‘A’ in this class for the semester!! • Seriously!

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