1. Warm Up Show all definite integrals!!!!! 1)Calculator Active: Let R be the region bounded by the graph of y = ln x and the line y = x – 2. Find the area of region R. 2) NO CALCULATOR: Let T be the region bounded by x = y 2 – 4y + 4, and x = y – 2. Determine the area of region T.

2. Area Between Curves Day 2

3. In the figure, R is the shaded region in the first quadrant bounded by the graph of y = 4ln(3 – x), the horizontal line y = 6 and the vertical line x = 2. Find the area of R. CALCULATOR ACTIVE

4. NO CALCULATOR Let R be the region in the first quadrant bounded by the graph of, the horizontal line y = 6 and the y-axis. Find the area of R.

5. Calculator Active Find the area of the region bounded by the graphs of ANS: 24

6. Calculator Active Let f and g be the functions given by f(x) = ¼ + sin(πx) and g(x) = 4 – x. Let R be the region in the first quadrant enclosed by the graphs of f and g and the y – axis and let S be the region in the first quadrant enclosed by the graphs of f and g. 1)Find the area of region R. 2)Find the area of region S.

7. Find the area of the region R in the first quadrant that is bounded by the x-axis, the line y = x – 2 and Sub-regions then Change variables NO CALCULATOR ANS: 10/3

8. Find the area of the region enclosed by the graphs of y = x 3 and x = y 2 – 2 CALCULATOR ACTIVE ANS: 4.215