Question

Problem1 A right circular cylinder (i.e., a "normal" cylinder) has radius 3 m and height 4 m. Using integrals, find numerical values for its a. volume, b. mass if its density is p(?)n appropriate units, and c. moment of inertia about the cylinder's axis. 20 Problem 2 The integral IsJo-* dx is notorious for not having an analytical solution. However, there's a clever trick to calculate definite integrals: instead of calculating I itself, it's easier to calculate I2. To do this, write the definition for 1, then multiply it by the same definition, but use y instead of x. (After all, the independent variable is a dummy variable, as it's integrated over.) Combine the integrals into a 2D integral, then change variables to polar coordinates and solve. Take the answer, and the square root is the value of I. Using this technique, calculatedx Problem 3 Find the mass of the solid inside the ellipsoid + +-1 ifthe density is pxyz Problem 4 Find the area of the plane x-2y+5-13 cut out by the cylinder x2y-9

Answer 1