EXTRA CREDIT: +5 points
Semester 2 Unit 1 – 1-1 WKST Name:
Area Between Curves.
A Graphing Calculator is required for these problems.
1. [2006 AB – Calculator OK] Let R be the shaded region bounded by the graph of [pic] and the line [pic], as shown above. Find the area of R.
2. [2005 AB – Calculator OK] Let f and g be the functions given by [pic] and [pic]. Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of f and g , and let S be the shaded region in the first quadrant enclosed by the graphs of f and g, as shown in the figure above.
(a) Find the area of R.
(b) Find the area of S.
3. [2004 AB – Calculator OK]
Let f and g be the functions given by [pic] and [pic]. The graphs of f and g are shown in the figure above. Find the area of the shaded region enclosed by the graphs of f and g .
4. [2002 AB – Calculator OK] Let f and g be the functions given by [pic] and [pic].
(a) Find the area of the region enclosed by the graphs of f and g between [pic] and [pic].
(b) Let h be the function given by [pic]. Find the absolute minimum value of [pic] on the closed interval [pic], and find the absolute maximum value of [pic] on the closed interval [pic]. Show the analysis that leads to your answers.
5. [2001 AB – Calculator OK] Let R and S be the regions in the first quadrant shown in the figure above. The region R is bounded by the x-axis and the graphs of [pic] and [pic]. The region S is bounded by the y-axis and the graphs of [pic] and [pic].
(a) Find the area of R.
(b) Find the area of S.
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x
O
ANSWERS:
1) 1.949 3) 1.133
2a) 0.0648 4a) 1.223
b) 0.410 b) min value: 2.330
max value: e
5a) 0.729
b) 1.161
R
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