' ******************************************************

' *   PROGRAM TO COMPARE AVERAGE VALUES OF CURVES OF   *

' *   THE FORM (Y = X^N) AS OBTAINED BY:               *

' *   1)   THE INTEGRAL CALCULUS                       *

' *   2)   SUMMATION DIVIDED BY N                      *

' *   3)   TRAPEZOIDAL RULE                            *

' ******************************************************

CLS : DEFDBL A-Z

INPUT " POWER TO RAISE INDEPENDENT VARIABLE TO IS "; N

INPUT " CALCULATE OVER DOMAIN ZERO TO (X MAX.=INTEGER)"; XMAX

10 PRINT : PRINT

INPUT " USE A STEP SIZE OF: (E.G., 0.5)"; SZ

PRINT : PRINT

PRINT "THE MEAN VALUE DETERMINED BY CALCULUS IS "; (XMAX ^ (N + 1) / (N + 1)) / XMAX

PRINT

' ******************************************************

YT = 0 ' INITIALIZE ACCUMULATOR

FOR I = 0 TO XMAX STEP SZ ' SOLVE ARITHMETIC MEAN

YT = YT + I ^ N

NEXT

YAV = YT / (XMAX / SZ + 1)' ADD 1 TO COUNT THE "ZERO" DATA POINT

PRINT "THE ARITHMETIC MEAN IS "; YAV: PRINT

YT = YT - (XMAX ^ N / 2): YAV = SZ * YT / XMAX

' ******************************************************

PRINT "THE AVERAGE DETERMINED BY THE TRAPEZOIDAL RULE IS "; YAV

PRINT "MORE (Y/N)";

90 A$ = INKEY$: IF A$ = "" THEN 90

IF A$ = "Y" OR A$ = "y" THEN 10



END





