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Arc Length and Surface Area

Arc Length and Surface Area. Lesson 7.4. What is another way of representing this?. Why?. Arc Length. We seek the distance along the curve from f(a) to f(b) That is from P 0 to P n The distance formula for each pair of points. P 1. P i. P n. •. P 0. •. •. •. •. •. b. a.

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Arc Length and Surface Area

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  1. Arc Length and Surface Area Lesson 7.4

  2. What is another way of representing this? Why? Arc Length • We seek the distance along the curve fromf(a) to f(b) • That is from P0 to Pn • The distance formula for each pair of points P1 Pi Pn • P0 • • • • • b a

  3. Arc Length • We sum the individual lengths • When we take a limit of the above, we get the integral Note the New Spreadsheet Assignment

  4. Arc Length • Find the length of the arc of the function for 1 < x < 2

  5. Surface Area • Suppose we rotate thef(x) from slide 2 aroundthe x-axis • A surface is formed • Think of the surface as a series of circles • What is circumference at xi? P1 Pi Pn • P0 • • • • • • xi b a

  6. Surface Area • We add the circumferences of all the circles • From a to b • Over entire length of the curve

  7. Surface Area • Consider the surface generated by the curve y2 = 4x for 0 < x < 8 about the x-axis

  8. Surface Area • Surface area =

  9. Limitations • We are limited by what functions we can integrate • Integration of the above expression is not trivial • We will come back to applications of arc length and surface area as new integration techniques are learned

  10. Assignment • Lesson7.4 • Page 282 • Exercises 1 – 13 odd, 14

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