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Trapezoidal Rule Revisited

Trapezoidal Rule Revisited. Using integrals to find area works extremely well as long as we can find the antiderivative of the function. Sometimes, the function is too complicated to find the antiderivative.

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Trapezoidal Rule Revisited

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  1. Trapezoidal Rule Revisited

  2. Using integrals to find area works extremely well as long as we can find the antiderivative of the function. Sometimes, the function is too complicated to find the antiderivative. At other times, we don’t even have a function, but only measurements taken from real life. What we need is an efficient method to estimate area when we can not find the antiderivative.

  3. Actual area under curve:

  4. Approximate area: Left-hand rectangular approximation: (too low)

  5. Approximate area: Right-hand rectangular approximation: (too high)

  6. Trapezoidal approximation: The trapezoidal approximation is also the average of the left and right sum! (still to high)

  7. Trapezoidal Rule: ( h = width of subinterval ) This is the average of the left and right Riemann sums.

  8. A pump connected to a generator operates at a varying rate, depending on how much power is being drawn from the generator to operate other machinery. The rate (gallons per minute) at which the pump operates is recorded at 5-minute intervals for one hour as shown in the table. How many gallons were pumped during that hour?

  9. Do now: P364 #14, 18

  10. Approximate the area under the curve on the interval [0,1] using the Trapezoidal Rule and 10 subintervals. (Use your calculator program.)

  11. Approximate the area under the curve on the interval [1,5] by finding the midpoint Riemann Sum using 4 subintervals. (By hand, then check with calculator.) 45

  12. Homework P363 #1-7 odd, 10, 13,15,17,18

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