Consider the volume V of the solid generated by rotating the region bounded by y = 3111(22) for I E [01%]: and y = 1 around the yaxis. In this problem you may use any formula from lectures. {a} (1 point) Sketch the region of interest. (b) [3 points} Express the volume as an integral with respect to a: by slicing the region :13 E [mar/2]. {c} [3 points} Express the volume as an integral with respect to y by slicing the region y E [0, 1]. (d) [3 points} Determine 1 (arcsin(t])2 alt. A trail runner tries to run a hiking trail in record time. Consider a path through the mountains from a: = A to :1', : Bthat is modelled by the function rs). y A B {a} {3 points} Assume first that the trail hiker runs a constant velocity I}. Write down an expression for total time T that it takes the trail runner to run the path from a: = Ato a": = B. (b) [7 points} Now let's try to model the velocity function more accurately. Suppose the velocity of the trail runner at any given point is given by: 253 to") 2 M where 3 is the slope [inclination]r fl is the height {altitude}; and d is the distance from the starting point. Using the slicing method in detailJ find an expression for the total time T it takes the runner to complete the path from $=At0$=B