6.6_Area_Between_Graphs_summer

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

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
6. Calculate the area between the line f(x) = -3x - 1 and the exponential curve
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

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)...
View Full Document

{[ snackBarMessage ]}

Page1 / 10

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

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online