EXTRA CREDIT: +5 points



Semester 2 Unit 1 – 1-1 WKST Name:

Area Between Curves.

A Graphing Calculator is required for these problems.

1. 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. 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 .

3. 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.

4. 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. 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

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ANSWERS:

1) 1.949 4a) 1.223

2) 1.133 b) min value: 2.330

3a) 0.0648 max value: e

b) 0.410 5a) 0.729

b) 1.161

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