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95 Set up, but do not calculate, the integral that represents the surface area of the surface obtained when the curve y = x, 1 x 4, is rotated about the x-axis 4 (a) 1 2 1/sqr tx 1 + x 2 dx 4 (b) 1 2 x 1 + [1/(4x)] dx 4 (c) 1 2 x 1 + 4x dx 4 (d) 1 2 x 1 + 4x 2 dx 4 (e) 1 2 x 1 + [1/(4x 2 )] dx 96 A swimming pool is rectangular in shape with vertical sides The bottom of the pool has dimensions 20 feet by 40 feet, and the pool is 10 feet deep The pool is full Calculate the total hydrostatic pressure on that portion of the short side of the pool between depths 2 feet and 5 feet (a) 12104 (b) 13104 (c) 11104 (d) 10014 (e) 10204

int Sample(int accountId, string name = "user", int userId) { // Error!

Because name is optional, userId must come before name (or userId must also be optional)

Part I:

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In addition to methods, optional arguments can be also used in a constructor, indexer, or delegate (Indexers and delegates are described later in this book) One benefit of optional arguments is that they enable the programmer to more easily manage complex method calls and constructor invocations Quite frequently, a method will specify more parameters than are required for its most common usage In many cases, through the careful use of optional arguments, some of those parameters can be made optional This means that you need pass only those arguments that are meaningful to your situation, rather than all of them, as would otherwise be required Such an approach streamlines the method and makes it easier for the programmer

97 Give the trapezoidal rule approximation to the integral uniform partition having four intervals 2 2 2 2 2 (a) [1/4] e 0 + 2e (1/2) + 4e (1) + 2e (3/2) + e 2 (b) e 0 + 2e (1/2) + 2e (1) + 2e (3/2) + e 2

In some cases, optional arguments can provide an alternative to method overloading To understand why, again consider the OptArgMeth( ) method just shown Prior to the addition of optional arguments to C#, you would need to create three different versions of OptArgMeth( ) to achieve the same functionality as the one version shown earlier These versions would have the following declarations:

static void OptArgMeth(int alpha) static void OptArgMeth(int alpha, int beta) static void OptArgMeth(int alpha, int beta, int gamma)

These overloads enable the method to be called with one, two, or three arguments (The bodies of the methods would have to provide the values of beta and gamma when they are not passed) While it is certainly not wrong to implement OptArgMeth( ) s functionality using overloading, the use of optional arguments is a better approach Of course, not all overloading situations lend themselves to such an approach

2 2 2 2 2 2 2 2 2

One problem that can result when using optional arguments is ambiguity This can occur when a method that has optional parameters is overloaded In some cases, the compiler may not be able to determine which version to call when the optional arguments are not specified For example, consider the following two versions of OptArgMeth( ):

static void OptArgMeth(int alpha, int beta=10, int gamma = 20) { ConsoleWriteLine("Here is alpha, beta, and gamma: " + alpha + " " + beta + " " + gamma); } static void OptArgMeth(int alpha, double beta=100, double gamma = 200) { ConsoleWriteLine("Here is alpha, beta, and gamma: " + alpha + " " + beta + " " + gamma); }

Notice that the only difference between the two versions is the types of beta and gamma, which are the optional parameters In the first version, their type is int In the second version, it is double Given these two overloads, the following call to OptArgMeth( ) is ambiguous:

8: