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Question 1: The base of a solid is the region in the first and second quadrants bounded by the graph of y = 1 - x² and the x-axis. If cross-sections of the solid perpendicular to the x-axis are squares, what is the volume of the solid?

Question 2:

t(hours)	0	.5	1	1.5	2	2.5	3
v(miles/hour)	32	30	16	22	20	24	26

A speedboat travels on a river. Its speed v, in miles per hour, at certain times is given in the table above. Using a left Riemann sum, what is the approximation of the total distance traveled by the speedboat from t = .5 to t = 3?

Question 3: At what value of x are the the tangent lines to the graphs of f(x) = ln(x) and g(x) = 6^x parallel?

Question 4: What is the average value of the function f(x) = sin²(3x) + x on the interval [0, ¶]?

Question 5: The base of a solid is the region in the first quadrant bounded by the graph of y = -x² + 5x - 4 and the x-axis. If cross-sections of the solid perpendicular to the x-axis are equilateral triangles, what is the volume of the solid?