1. The curve shown below can be expressed both as a function of z, y = f(2), and as a function of y, r = h(y). The region bounded by this curve and the axes is rotated about the r-axis to form a solid with volume V. (2 points) Find an expression for V using both 1.34 the disk method and the shell method. Draw y - /x) diagrams to explain your integrands. 2. (4 points) Consider the region bounded by a = 4y -y" and the y-axis such that y 2 0. Find the volume of the solid formed by rotating the region about a) the vertical line x = -1 b) the horizontal line y = -2. Please include diagrams to help justify your integrals. 3. In the last homework assignment, you computed the volume of the solid obtained by rotating the region inside r2 + (y -4) =9 about the r-axis using the washer method. (2 points) Set up, but do not evaluate, an integral for the volume of the solid of revolution using the shell method. 4. (2 points) Calculate the average value of each function over the given interval. Hint: use the identity tan (x) = sec?(x) - 1 a) f(x) = rtan?(r), on the interval |0, b) g(x) = vreva, on the interval [0, 4]