6. Set up (but do not solve) the integral for the arc length of the function f(x) = 111(sinx + 2) on the interval [2, 15]. 7. Set up (but do not solve) the integral(s) for region bounded by y = x3 + 4, the vertical lines 35 = 0 and x = 4, and the x-axis When: a. The region is the base of a solid with square cross-sections J. to the x-axis. b. The region is rotated around the y-aXis and sliced horizontally. c. The region is rotated around the vertical line 96 = 5 and is sliced vertically. 8. A giant container in a NerdzTM production factory is in the shape of an inverted cone (like it's holding ice-cream). It is 15 m deep and has a radius at the top of 5 m. It's filled to the top with NerdzTM (very small candy bits) and the density of the candy depends on the depth k x, by the formula p(x) = 3 _ 1.490.23: mga gives the total mass of NerdzTM in the container if the x-axis is at the top of the container pointing downward. . Set up (but do not solve) the integral that 9. A trough (an open top water container) is 25 m long and 2 m high. The vertical cross- sections of the trough parallel to the ends is shaped like the graph 3! = $952 on the interval [ 2, 2] . Set up (but do not solve) the integral that gives the total work required to pump the water over the top of the trough supposing it is full of water