1 / 13

Area Connection and the FTC

Area Connection and the FTC. Section 5.4b. How to Find Total Area Analytically. To find the area between the graph of y = f ( x ) and the x -axis over the interval [ a , b ] analytically,. 1. Partition [ a , b ] with the zeros of f ,. 2. Integrate f over each subinterval,.

regis
Download Presentation

Area Connection and the FTC

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 Connectionand the FTC Section 5.4b

  2. How to Find Total Area Analytically To find the area between the graph of y = f (x) and the x-axis over the interval [a, b ] analytically, 1. Partition [a, b ] with the zeros of f, 2. Integrate f over each subinterval, 3. Add the absolute values of the integrals.

  3. How to Find Total Area Numerically To find the area between the graph of y = f (x ) and the x-axis over the interval [a, b ] numerically, evaluate NINT ( |f (x)|, x, a, b )

  4. Guided Practice Find the area of the region between the given function and the x-axis for the given interval. How about a graph? Over [0, 2]: 4 Antiderivative: 1 2 3 –5

  5. Guided Practice Find the area of the region between the given function and the x-axis for the given interval. How about a graph? Over [0, 2]: 4 1 2 3 –5

  6. Guided Practice Find the area of the region between the given function and the x-axis for the given interval. How about a graph? Over [2, 3]: 4 1 2 3 –5

  7. Guided Practice Find the area of the region between the given function and the x-axis for the given interval. How about a graph? Total area of the region: 4 1 2 3 Verify with NINT!!! –5

  8. Guided Practice Find the area of the region between the given function and the x-axis for the given interval. The graph? Total Area = 8

  9. Guided Practice For the following integral, (a) can the FTC (part 2) be used to evaluate the integral, and (b) does the integral have a value (if so, what is it? – explain!)? • The FTC (part 2) cannot be used, because the integrand is discontinuous at x = 3!!! Evaluate this integral graphically!!!

  10. Guided Practice For the following integral, (a) can the FTC (part 2) be used to evaluate the integral, and (b) does the integral have a value (if so, what is it? – explain!)? This integral does not have a value!!! Why not???

  11. Guided Practice For the following integral, (a) can the FTC (part 2) be used to evaluate the integral, and (b) does the integral have a value (if so, what is it? – explain!)? This integral does exist, because the region is bounded!!! (evaluate the integral numerically)

  12. Guided Practice Find the area of the shaded region for #26 on p.286. Total Area

  13. Guided Practice Find the area of the shaded region for #28 on p.286. Calculate the area under the sine curve over the interval, then subtract the area of the rectangle… Total Area

More Related