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Description Returns the index of the last occurrence of value within the invoking string The search proceeds in reverse order, beginning at the index specified by startIndex and running for count elements Returns 1 if value is not found Culture-sensitive searching is used Returns the index of the last occurrence of value within the invoking string How the search is performed is specified by comparisonType Returns 1 if value is not found Returns the index of the last occurrence of value within a range of the invoking string The search proceeds in reverse order, beginning at the index specified by startIndex and stopping at zero How the search is performed is specified by comparisonType Returns 1 if value is not found Returns the index of the last occurrence of value within the invoking string The search proceeds in reverse order, beginning at the index specified by startIndex and running for count elements How the search is performed is specified by comparisonType Returns 1 if value is not found Returns the index of the last occurrence of any character in anyOf that is found within the invoking string Returns 1 if no match is found Ordinal searching is used Returns the index of the last occurrence of any character in anyOf that is found within the invoking string The search proceeds in reverse order, beginning at the index specified by startIndex and stopping at zero Returns 1 if no match is found Ordinal searching is used Returns the index of the last occurrence of any character in anyOf that is found within the invoking string The search proceeds in reverse order, beginning at the index specified by startIndex and running for count elements Returns 1 if no match is found Ordinal searching is used Returns true if the invoking string begins with the string passed in value Otherwise, false is returned Culture-sensitive searching is used Returns true if the invoking string begins with the string passed in value Otherwise, false is returned How the search is performed is specified by comparisonType Returns true if the invoking string begins with the string passed in value Otherwise, false is returned If ignoreCase is true, the search ignores case differences Otherwise, case differences matter The search is conducted using the cultural information passed in culture.

// Constructor for TwoDShape public TwoDShape(double w, double h) { Width = w; Height = h; } // Properties for Width and Height public double Width { get { return pri_width; } set { pri_width = value < 0 -value : value; } } public double Height { get { return pri_height; } set { pri_height = value < 0 -value : value; } } public void ShowDim() { ConsoleWriteLine("Width and height are " + Width + " and " + Height); } } // A derived class of TwoDShape for triangles class Triangle : TwoDShape { string Style; // Call the base class constructor public Triangle(string s, double w, double h) : base(w, h) { Style = s; } // Return area of triangle public double Area() { return Width * Height / 2; } // Display a triangle's style public void ShowStyle() { ConsoleWriteLine("Triangle is " + Style); } } class Shapes4 { static void Main() { Triangle t1 = new Triangle("isosceles", 40, 40); Triangle t2 = new Triangle("right", 80, 120); ConsoleWriteLine("Info for t1: "); t1ShowStyle(); t1ShowDim(); ConsoleWriteLine("Area is " + t1Area());

I have reviewed your letter of complaint (seven words)

Part I:

Resubstituting the expression for ( x) yields that 1 cos x dx = ln |3 sin x 4| + C 3 sin x 4 3

ConsoleWriteLine(); ConsoleWriteLine("Info for t2: "); t2ShowStyle(); t2ShowDim(); ConsoleWriteLine("Area is " + t2Area()); } }

public Triangle(string s, double w, double h) : base(w, h) {

In this version, Triangle( ) calls base with the parameters w and h This causes the TwoDShape( ) constructor to be called, which initializes Width and Height using these values Triangle no longer initializes these values itself It need only initialize the value unique to it: Style This leaves TwoDShape free to construct its subobject in any manner that it chooses Furthermore, TwoDShape can add functionality about which existing derived classes have no knowledge, thus preventing existing code from breaking Any form of constructor defined by the base class can be called by base The constructor executed will be the one that matches the arguments For example, here are expanded versions of both TwoDShape and Triangle that include default constructors and constructors that take one argument

For clarity we take ( x) = sin x, ( x) = cos x Then the integral becomes ( x) dx = ln | ( x) | + C ( x) Resubstituting the expression for yields the solution: cot x dx = ln | sin x| + C

// Add more constructors to TwoDShape using System; class TwoDShape { double pri_width; double pri_height; // Default constructor public TwoDShape() { Width = Height = 00; } // Constructor for TwoDShape public TwoDShape(double w, double h) { Width = w; Height = h; } // Construct object with equal width and height public TwoDShape(double x) { Width = Height = x; } // Properties for Width and Height public double Width { get { return pri_width; } set { pri_width = value < 0 -value : value; } }

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