1 of 1 Math 152 Lab 5 Use MATLAB to solve cach problem. Some of the commands you may need on this assignment are: syms, int, solve, partfrac, and double 1. (3 points) Consider the function f(r)- where a is a positive real constant ztvr -- (a) Find the area bounded between the curve and the r-axis for any value of a on the interval 2a, 4a (b) For what valne of a is the area under the curve exactly 5? 2. (4 points) Consider the function f(x) where a is a positive real constant +0,7, (a) Find the volune of the solid formed when the region bounded by f, aa, and the r-axis is rotated about the y-axis. (b) Find the volune of the solid formed when the region bounded by , -a, and the r-axis is rotated about the z-axis. (c) For what value of a are these two volumes cqual? 3. (3 points) r3-Ar +3 a-5(2 +3)(2+5) (a) Find the partial fraction decomposition of the function f(z) = 2+2x+where a is a (b) Find the partial fraction decomposition of the function g(z) = 1) positive real constant. (c) For what value of a, does g(z) dr = 1