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1 #include <iostream>
2 #include <cmath>
3 using namespace std;
4
5 //equations
6 double f1(double x){
7 return ((2*pow(x,5))+(pow(x,3))-(10*x)+(2));
8 }
9
10 double f2(double x){
11 return ((6*pow(x,2))-(x)+(10));
12 }
13
14 double f3(double x){
15 return ((5*x)+(3));
16 }
17
18 double f4(double x){
19 return ((2*pow(x,3))+(120));
20 }
21
22 double f5(double x){
23 return (2*pow(x,2));
24 }
25
26
27
28
29 //this function calculates the area of rectangles and adds them up
30 double rect_area(double a, double b, double n, int func_choice){
31 double area =0;
32 double x=0;
33 double width;
34 width =((b-a)/n);
35
36 for(int i=1; i<=n; i++){
37 x+=width;
38 if(func_choice==1){
39 area += (f1(x) * width);
40 }
41 if(func_choice==2){
42 area+= (f2(x) * width);
43 }
44 if(func_choice==3){
45 area+= (f3(x) * width);
46 }
47 if(func_choice==4){
48 area+= (f4(x) * width);
49 }
50 if(func_choice==5){
51 area+= (f5(x) * width);
52 }
53 }
54 return area;
55 }
56
57 //this function calculates the area of trapezoids and adds them up
58 double trap_area(double a, double b, double n, int func_choice){
59 double area = 0;
60 double x = 0;
61 double width;
62 width = ((b-a)/n);
63
64 for(int i; i<=n; i++){
65 x+=width;
66 if(func_choice==1){
67 area += (f1(x) * width);
68 }
69 if(func_choice==2){
70 area+= (f2(x) * width);
71 }
72 if(func_choice==3){
73 area+= (f3(x) * width);
74 }
75 if(func_choice==4){
76 area+= (f4(x) * width);
77 }
78 if(func_choice==5){
79 area+= (f5(x) * width);
80 }
81 }
82 return area;
83 }
84
85
86 int main(){
87 int reset;
88 int func_choice;
89 double a, b;
90 int method;
91 double rect_num;
92 double trap_num;
93 double width;
94 double area = 0;
95
96 //do while loop to repeat if user wants
97 do{
98 //user picks a function
99 cout << "Choose a function(1,2,3,4,5,other(quit)): " << endl;
100 cout << "f1(x)=2x^5 + x^3 - 10x +2" << endl;
101 cout << "f2(x)=6x^2 -x + 10" << endl;
102 cout << "f3(x)=5x + 3 " << endl;
103 cout << "f4(x)=2x^3 +120 " << endl;
104 cout << "f5(x)=2x^2 " << endl;
105 cin >> func_choice;
106
107 //if user chooses something other than a given number, program quits
108 if(func_choice < 1 || func_choice > 5){
109 return 0;
110 }
111
112 //method of integration
113 cout <<"Which method would you like to use?(rectangle(1), trapezoid(2), both(3)): " << endl;
114 cin >> method;
115
116 //starting values
117 cout <<"Input a start value: " << endl;
118 cin >> a;
119 cout <<"Input an end value: " << endl;
120 cin >> b;
121
122 //calculates area based on users choice
123 switch(method){
124 case 1:
125 cout <<"How many rectangles would you like?" << endl;
126 cin >> rect_num;
127 area = rect_area(a,b,rect_num,func_choice);
128 cout << "The area of " << func_choice << " is " << area << " from " << a << " to " << b << " with " << rect_num << " rectangles " << endl;
129 break;
130
131 case 2:
132 cout <<"How many trapezoids would you like?" << endl;
133 cin >> trap_num;
134 area = trap_area(a,b,trap_num,func_choice);
135 cout << "The area of " << func_choice << " is " << area << " from " << a << " to " << b << " with " << trap_num << " trapezoids " << endl;
136 break;
137
138 case 3:
139 cout <<"How many rectangles would you like?" << endl;
140 cin >> rect_num;
141 cout <<"How many trapezoids would you like?" << endl;
142 cin >> trap_num;
143
144 area = rect_area(a,b,rect_num,func_choice);
145 cout << "The area of " << func_choice << " is " << area << " from " << a << " to " << b << " with " << rect_num << " rectangles " << endl;
146 area = trap_area(a,b,trap_num,func_choice);
147 cout << "The area of " << func_choice << " is " << area << " from " << a << " to " << b << " with " << trap_num << " trapezoids " << endl;
148 break;
149
150 default:
151 while(method<1, method>3){
152 cout << "not a valid input" << endl;
153 cout << "please choose a given method" << endl;
154 method =0;
155 cin >> method;
156 }
157 }
158
159 //question to recieve input for the condition of the do while loop
160 cout << "would you like to compute another area?(1 for yes, 0 for no)" << endl;
161 cin >> reset;
162
163 }while(reset==1);
164 return 0;
165 }
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