1. A circle, centered at the origin with radius r, is shown below along with the equation for the top half of the circle. Whole circle: x2+ 312: r2 Top half of circle: y = \\/ r2 x2 a. Suppose the top half of the circle is rotated about the x-axis to create a sphere. Setup at r3 and solve a definite integral that derives the formula for volume of a sphere (using the 3 disk, washer, or shell method). b. Suppose the whole circle is graphed. Setup and solve a definite integral that derives the C = 2 31- r formula for circumference of a circle (using the arc length formula). c. Suppose the top half ofthe circle is rotated about the x-axis to create a sphere. Setup 2 and solve a definite integral that derives the formula for surface area of a sphere (using A = 4 .71" r the surface area formula). 2. A thin plate is described (and enclosed) by the region below. Region: y=x2+ 1, x= 2, x=2, x axis a. Where is the center of mass when the density is constant? b. Where is the center of mass when the density is variable? 5( I) =x + 1 Reminder: Complete all work in your handwriting Sketch ALL two-dimensional graphs by hand and fully label each one Show ALL calculus/algebra work Give exact answers (do NOT give decimal approximations)