Ultimate Calculus Program: Program includes Rolles, Trapezoidal, Mean Value, Rieman Sum, and Integral Equations. A must need for AP Calculus.

    
Rolles
    
Mean Value
    
Trap Rule
    Riemann Sum
    
Integral Equat
    Reference
f(a)=f(b)f'(c)=f(b)-f(a)
 f(c)=0         b-a


AP Calcculus

1. Lbl A        Menu AP Calc
2. ClrHome:Menu("AP Calc","Rolles",1,"Mean Value",2,"Trap Rule",3,"Riemann Sum",4,"Integral Equat",5,"Exit",7)
3. Lbl 5        Integral Equat
4. ClrHome:FnOff
5. ClrDraw:AxesOff:ZDecimal
6. Text(2,15,"Integral Formulas
7. Horizontal 2.3
8. Text(10,5,"c=c*n
9. Text(20,5,"i =n(n+1)/2
10. Text(30,5,"i^2 =n(n+1)(2n+1)/2
11. Text(40,5,"i^3 =n^2(n+1)^2/4
12. Text(50,5,"mp =f(Xi+Xi-1/2)^X
13. Pause
14. ClrDraw:AxesOn:FnOn :ClrHome:Goto A        Menu AP Calc
15.
Lbl 4        Riemann Sum
16. ClrHome
17. Input "A= ",S
18. Input "B= ",E
19. Input "N= ",N
20. 0->Z
21. E-S->W
22. If W<=0
23. Then
24. S->C
25. E->S
26. C->E
27. E-S->W
28. End
29. W/N->Y
30. S->X
31. E->A
32. Disp "LRAM"        left-hand rectangular approximation
33. 0->Z
34. While X/=A
35. abs(Y1)+Z->Z
36. X+Y->X
37. End
38. Y*Z->Z
39. Disp Z
40. Y/2->B
41. S+B->X
42. E+B->A
43. Disp "MRAM"        midpoints on the curve
44. 0->Z
45. While X/=A
46. abs(Y1)+Z->Z
47. X+Y->X
48. End
49. Y*Z->Z
50. Disp Z
51. S+Y->X
52. E+Y->A
53. Disp "RRAM"        right-hand rectangular approximation
54. 0->Z
55. While X/=A
56. abs(Y1->)+Z->Z
57. X+Y->X
58. End
59. Y*Z->Z
60. Disp Z
61. Pause :Goto A        Menu AP Calc
62.
Lbl 3        Trap Rule
63. Radian
64. ClrHome
65.
Lbl 1        Rolles
66. Menu("Trapezoidal","Rule",B,"Solver",C,"Back",A)
67. Lbl B
68. ClrHome:FnOff :AxesOff:ZDecimal:Text(1,3,"Trapezoidal Rule"
69. Horizontal 2.3
70. Text(10,1,"(B-A)/N=X
71. Text(20,1,"1/2 X{f(A)+2f(B/N)+...+f(B)}
72. Pause :ClrDraw:AxesOn:Goto 1
73. Lbl C
74. 0->Y:0->Z:0->theta:0->D:0->U:1->C:0->X
75. ClrHome
76. Input "A= ",A
77. Input "B= ",B
78. Input "N= ",N
79. ((B-A)/N)->D
80. Input "Y1=",Str1        "f(x)= ",Str1
81. Str1->Y1
82. A+D->Y:D->X
83. While C<=(N-1)
84. 2Y1(Y)->theta
85. theta+Z->Z
86. X+Y->Y
87. C+1->C
88. End
89. (Y1(A)+Y1(B))->J:J+Z->N
90. (1/2)D(N)->U
91. Disp "Ans= ",U
92. Pause :Goto 1
93. Lbl 7
94. ClrHome:Stop
95.
Lbl 1        Rolles
96. CoordOff
97. GridOff
98. AxesOff
99. LabelOff
100. 1774.118->Ymin
101. 4815.81->Xmin
102. 4815.82->Xmax
103. 17774.119->Ymax
104. ClrHome
105. Disp "FIND ROLLES THM."
106. Input "Y1=",Str1        "f(x)= ",Str1
107. Str1->Y1
108. Disp "","A<=X<=B"
109. Input "A? ",A
110. Input "B? ",B
111. ClrHome
112. Text(0,0,"Y1=",Str1," / ",A,"<=X<=",B
113. A-.12->A
114. B+.2->B
115. 0->dim(L1
116. (B-A)/20->S
117.
118. A->N
119. Text(6,0,"SCANNING...
120. .00001->H
121. While N+S 122. If (nDeriv(Y1,X,N,H)>0 and 0>=nDeriv(Y1,X,N+S,H)) or (nDeriv(Y1,X,N,H)<0 and 0<=nDeriv(Y1,X,N+S,H))
123. Then
124. dim(L1)+1->dim(L1
125. N->L1(dim(L1))
126. End
127. N+S->N
128. Text(6,40,(N-A)/(B-A)100,"PCT
129. End
130. Text(12,0,dim(L1)," SOLUTIONS FOUND... "
131. For(X,1,dim(L1
132. L1(X)->N
133. (B-A)/100->S
134. While S>.00001
135. If (nDeriv(Y1,X,N,H)<0 and 0<=nDeriv(Y1,X,N+S,H)) or (nDeriv(Y1,X,N,H)>0 and 0>=nDeriv(Y1,X,N+S,H))
136. S/10->S
137. N+S->N
138. End
139. Text(18+6fPart((X-1)/7)7,47iPart((X-1)/7),"X=",int(N1000+.5)/1000
140. End
141. Pause
142. Goto A        Menu AP Calc
143.
Lbl 2        Mean Value
144. CoordOff
145. GridOff
146. AxesOff
147. LabelOff
148. 1774.118->Ymin
149. 4815.81->Xmin
150. 4815.82->Xmax
151. 17774.119->Ymax
152. ClrHome
153. Disp "FIND MEAN VAL."
154. Input "Y1=",Str1        "f(x)= ",Str1
155. Str1->Y1
156. Disp "","A<=X<=B"
157. Input "A? ",A
158. Input "B? ",B
159. ClrHome
160. Text(0,0,"Y1=",Str1," / ",A,"<=X<=",B
161. Text(8,0,"(F(B)-F(A))/(B-A)
162. A->X:Y1->C
163. B->X:Y1->D
164. Text(14,0,"(",D,"-",C,")
165. Text(20,10,"/(",B,"-",A,")
166. Text(28,0,(D-C)/(B-A)," = SLOPE
167. 0->dim(L1
168.
169. (B-A)/20->S
170. (D-C)/(B-A)->E
171. A->N
172. Text(36,0,"SCANNING...
173. .00001->H
174. While N+S 175. If (nDeriv(Y1,X,N,H)>=E and E>=nDeriv(Y1,X,N+S,H)) or (nDeriv(Y1,X,N,H)<=E and 176. E<=nDeriv(Y1,X,N+S,H))
177. Then
178. dim(L1)+1->dim(L1
179. N->L1(dim(L1))
180. End
190. N+S->N
191. Text(36,40,(N-A)/(B-A)100,"PCT
192. End
193. Text(36,0,dim(L1)," SOLUTIONS FOUND... "
194. For(X,1,dim(L1
195. L(X)->N
196. (B-A)/100->S
197. While S>.00001
198. If (nDeriv(Y1,X,N,H)=E and E>=nDeriv(Y1,X,N+S,H))
199. S/10->S
200. N+S->N
201. End
202. Text(36+6X,0,"X=",int(N1000+.5)/1000
203. End
204. Pause
205. Goto A        Menu AP Calc

Reference:
Integral equation
  In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.
Riemann sum
  In mathematics, a Riemann sum is an approximation of the area of a region, often the region underneath a curve.
Trapezoidal rule
  In numerical analysis, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) is a technique for approximating the definite integral
Mean value theorem
  In mathematics, the mean value theorem states, roughly: that given a planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.
Rolle's theorem
  In calculus, Rolle's theorem essentially states that any real-valued differentiable function that attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero.