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Warm up Problems 1) Approximate using left- and right- hand Riemann sums, n = 6. 2) 3) Find without a calculator.
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Using the Integral time (sec) velocity (m/sec) Integral = meters/sec * sec = meters
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Ex. Let, find the displacement and distance travelled from t = 0 to t = 6.
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Ex. Let, find the displacement and distance travelled from t = 0 to t = 1.5.
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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].
![Thm. The average value of a function f (x) over the interval [a,b] is Ex.](http://images.slideplayer.com./32/9805950/slides/slide_6.jpg "Find the average value of f (x) = sin 5x on [10,30]..")
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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) 020 331 628 924 1222 1521
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Properties of Integrals
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Ex. If, find
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