1 / 11

Area and the Definite Integral

Area and the Definite Integral. Lesson 7.3A. a. b. The Area Under a Curve. Divide the area under the curve on the interval [a,b] into n equal segments Each "rectangle" has height f(x i ) Each width is x The area if the i th rectangle is f(x i ) • x We sum the areas. •.

justis
Download Presentation

Area and the Definite Integral

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Area and the Definite Integral Lesson 7.3A

  2. a b The Area Under a Curve • Divide the area underthe curve on the interval [a,b] inton equal segments • Each "rectangle" has height f(xi) • Each width is x • The area if the i threctangle is f(xi)•x • We sum the areas •

  3. The SumCalculated • Consider the function2x2 – 7x + 5 • Use x = 0.1 • Let the = left edgeof each subinterval • Note the sum

  4. The Area Under a Curve • The accuracy of the summation will increase if we have more segments • As we increase n • As n gets infinitely large the summation is exact

  5. Upper limit of integration The integrand Lower limit of integration The Definite Integral • We will use another notation to represent the limit of the summation

  6. Example • Try • Use summation on calculator.

  7. Example • Note increased accuracy with smaller x

  8. Limit of the Sum • The definite integral is the limit of the sum.

  9. Practice • Try this • What is the summation? • Where • Which gives us • Now take limit

  10. Practice • Try this one • What is x? • What is the summation? • For n = 50? • Now take limit

  11. Assignment • Lesson 7.3A • Page 458 • Exercises 6 – 20 all

More Related