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The symbol is called an integral sign (the symbol is in fact an elongated S ) and the symbol dx plays a traditional role to remind us what the variable is We call an expression like f (x) dx an inde nite integral The name comes from the fact that later on we will have a notion of de nite integral that speci es what value C will take so it is more de nite in the answer that it gives EXAMPLE 41

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One question that is often raised when working with generics is whether the use of a generic class leads to code-bloat at runtime The simple answer is no The reason is that C# implements generics in a highly efficient manner that creates new constructed types only when they are needed Here is how the process works When a generic class is compiled into MSIL, it retains all of its type parameters in their generic form At runtime, when a specific instance of the class is required, the JIT compiler constructs a specific, executable code version of the class in which the type parameters are replaced by the type arguments Each instance of the class that uses the same type arguments will use the same executable code version For example, given some generic class called Gen<T>, then all Gen<int> objects will use the same executable code Thus, code-bloat is reduced and only those versions of the class that are actually used in the program will be created When a different constructed type is needed, a new version of the class is compiled

Part I:

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As you can see, the properties Count and Str are set via object initializer expressions The output is the same as that produced by the program in 8 and is shown here:

SOLUTION We know that we must guess a trigonometric function Running through the choices, cosine seems like the best candidate The derivative of cos x is sin x So we immediately see that cos x is a better guess its derivative is sin x But then we adjust our guess to F (x) = cos(3x + 1) to take into account the form of the argument This almost works: we may calculate that F (x) = 3 sin(3x + 1) We determine that we must adjust by a factor of 1/3 Now we can record our nal answer as 1 sin(3x + 1) dx = cos(3x + 1) + C 3 We invite the reader to verify that the derivative of the answer on the right-hand side gives sin(3x + 1) EXAMPLE 42

As explained in 8, the object initializer syntax is most useful when working with anonymous types generated by a LINQ expression In most other cases, you will use the normal constructor syntax

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Properties have some important restrictions First, because a property does not define a storage location, it cannot be passed as a ref or out parameter to a method Second, you cannot overload a property (You can have two different properties that both access the same variable, but this would be unusual) Finally, a property should not alter the state of the underlying variable when the get accessor is called Although this rule is not enforced by the compiler, violating it is semantically wrong A get operation should be nonintrusive

By default, the set and get accessors have the same accessibility as the indexer or property of which they are a part For example, if the property is declared public, then by default the get and set accessors are also public It is possible, however, to give set or get its own access modifier, such as private In all cases, the access modifier for an accessor must be more restrictive then the access specification of its property or indexer There are a number of reasons why you may want to restrict the accessibility of an accessor For example, you might want to let anyone obtain the value of a property, but allow only members of its class to set the property To do this, declare the set accessor as private For example, here is a property called MyProp that has its set accessor specified as private

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