6.6_Area_Between_Graphs_summer

# 6.6_Area_Between_Graphs_summer - g(x = e x on the...

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6.6 Area Between Graphs Warm-ups from 6.5 1. Evaluate the given definite integral 1 0 (x 3 – ½)/ ( x 4 – 2x +5) dx - 3/160 2. Find the average value of the function over [-1,2] f(x) = -4x 2 + 3x +1 - 3/2 3. The concentration of a certain drug in a patient’s bloodstream t hours after injection is 0.6t ( t 2 + 4) mg/cm 3

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Determine the average concentration over the first 3 hours after the drug is injected. Round to 3 decimals. (.118) 6.6 THEOREM Let f and g be continuous functions such that f(x) > g(x) on the interval [a.b] Then, the area of the region bounded above by y = f(x) and below by y = g(x) on [a,b] is given by: a b [f(x) – g(x)] dx 4. Find the area of the shaded region if f(x) = 3x 2 + x + 8 on the closed interval [ -3, 1]. (See Maple problem) ans:56
5. Find the area of the shaded region if f(x) = -6x 2 -16-2x 3 -4x + x 4 (See Maple problem) ans:864/5

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6. Calculate the area between the line f(x) = -3x - 1 and the exponential curve

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Unformatted text preview: g(x) = e x on the interval [0,1]. (See Maple problem) ans: 7. Calculate the area between the parabola f(x) = 2x 2 + 3x and the curve g(x) = -3e x on the interval [0,3]. Ans:3e 3 + 57/2 8. Calculate the area between the line f(x) = x + 3 and the line g(x) = -3/x on the interval [1,3] Ans: 3 ln(3) + 10 9. Find the area of the shaded region (see Maple problem) if f(x) = - 2x / (x 2 +4) on the closed interval [-3,4] Ans: ln(13)-2ln(2) + ln(5) 10. Set up an integral which represents the area between the parabola f(x) = -1/2 x 2 and the line g(x) = -x - 4. Enter answer in the form int(h(x),x=a to b) Ans: int(-1/2x 2 – (-x-4),x=-2 to 4) 11. Set up an integral which represents the area between the parabola f(x) = -2x 2 + 2x and the line g(x) = 2x- 2. Enter answer in the form int(h(x),x=a to b) Ans: int(-2x 2 +2x-(2x-2),x= -1 to 1)...
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6.6_Area_Between_Graphs_summer - g(x = e x on the...

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