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sec2 x dx 1 tan2 x 4 Evaluate each of the following inde nite trigonometric integrals (a) (b) (c) sin x cos2 x dx sin3 x cos2 x dx tan3 x sec2 x dx

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50 45 40 Displacement (mm) 35 30 25 20 15 10 5 0 0 50 100 150 200 250 y (deg) 300 350 400

Often you will want to cycle through the elements in a collection For example, you might want to display each element One way to do this is to use a foreach loop, as the preceding examples have done Another way is to use an enumerator An enumerator is an object that implements either the non-generic IEnumerator or the generic IEnumerator<T> interface IEnumerator defines one property called Current The non-generic version is shown here: object Current { get; } For IEnumerator<T>, Current is declared like this: T Current { get; } In both cases, Current obtains the current element being enumerated Since Current is a read-only property, an enumerator can only be used to retrieve, but not modify, the objects in a collection IEnumerator defines two methods The first is MoveNext( ): bool MoveNext( ) Each call to MoveNext( ) moves the current position of the enumerator to the next element in the collection It returns true if the next element is available, or false if the end of the collection has been reached Prior to the first call to MoveNext( ), the value of Current is undefined (Conceptually, prior to the first call to MoveNext( ), the enumerator refers to the nonexistent element that is just before the first element Thus, you must call MoveNext( ) to move to the first element) You can reset the enumerator to the start of the collection by calling Reset( ), shown here: void Reset( ) After calling Reset( ), enumeration will again begin at the start of the collection Thus, you must call MoveNext( ) before obtaining the first element In IEnumerator<T>, the methods MoveNext( ) and Reset( ) work in the same way Two other points: First, you cannot use an enumerator to change the collection that it is enumerating Thus, enumerators are read-only relative to the collection Second, any change to the collection under enumeration invalidates the enumerator.

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division Thus, in the first test, d is 2 and the modulus operation is performed The second test fails because d is set to zero, and the modulus operation is skipped, avoiding a divideby-zero error Finally, the normal AND operator is tried This causes both operands to be evaluated, which leads to a runtime error when the division-by-zero occurs Since the short-circuit operators are, in some cases, more efficient than their normal counterparts, you might be wondering why C# still offers the normal AND and OR operators The answer is that in some cases you will want both operands of an AND or OR operation to be evaluated because of the side effects produced Consider the following:

placement, as shown in Fig 715 and described in Table 71 Moreover, the displacement of the follower has an amplitude of 50 mm, and the phase and return phases are produced using a cycloidal motion (Angeles and Lopez-Caj n, 1991) For quick reference, the normal cycloidal motion is given as s (y ) = y - (1 2p ) sin 2py , 0 y 1 (786)

// Side effects can be important using System; class SideEffects { static void Main() { int i; bool someCondition = false; i = 0; // Here, i is still incremented even though the if statement fails if(someCondition & (++i < 100)) ConsoleWriteLine("this won't be displayed"); ConsoleWriteLine("if statement executed: " + i); // displays 1 // In this case, i is not incremented because the short-circuit // operator skips the increment if(someCondition && (++i < 100)) ConsoleWriteLine("this won't be displayed"); ConsoleWriteLine("if statement executed: " + i); // still 1 !! } }

(d) (e) (f)

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