Warm up Problems 1) Approximate using left- and right- hand Riemann sums, n = 6. 2) 3) Find without a calculator.

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Presentation transcript:

Warm up Problems 1) Approximate using left- and right- hand Riemann sums, n = 6. 2) 3) Find without a calculator.

Using the Integral time (sec) velocity (m/sec) Integral = meters/sec * sec = meters

Ex. Let, find the displacement and distance travelled from t = 0 to t = 6.

Ex. Let, find the displacement and distance travelled from t = 0 to t = 1.5.

Thm. The average value of a function f (x) over the interval [a,b] is Ex. Find the average value of f (x) = sin 5x on [10,30].

Ex. The temperature, in ºC, of a pond is a function W of time t. The table below shows the temperature at selected times. Approximate the average temperature over the time interval 0 ≤ t ≤ 15 using right-hand sums with 5 subintervals. tW(t)

Properties of Integrals

Ex. If, find