例題4-1 計算 exp(x) 在[0 , 1] 的定積分

'''
例題4-1 計算 exp(x) 在[0 , 1]的定積分
'''
import math

def  f(x) :
    return math.exp(x)

def computeT(a , b ,  n) :
    h = (b - a) / n
    T = 0.0
    for i in range (1 , n ):
        T += f(a + i * h)    #  //1 <= k <= n - 1
    return  (h *  0.5 * (  f(a) +  2 * T + f(b) )  )

n = 10       #//區間等分數
a = 0.0
b = 1.0      #//上下限
print("answer = {%10.6f}\n"  %( computeT(a, b, n) ) )

print("exp(x) 在[0, 1]的定積分={%10.6f}\n"  %(math.exp(1)-math.exp(0) ) )

print("誤差值={%10.6f}\n" % ( abs  (computeT(a, b, n) - (math.exp(1)-math.exp(0) ) )  )  )


'''
/*
    本實驗用梯形求積公式求sinx在[1, 2]的定積分。
*/
#include <stdio.h>
#include <math.h>

double f(double x){
    return sin(x);
}

double computeT(double a, double b, int n){
    double h = (b - a) / n, T = 0;

    for(int i = 1; i < n; i++)  T += f(a + i * h);  //1 <= k <= n - 1
    return h * (f(a) + 2 * T + f(b)) / 2;
}

int main(){
    int n = 8;  //區間等分數
    double a = 1, b = 2;  //上下限

    printf("answer = %f\n", computeT(a, b, n));
    return 0;
}
'''

輸出畫面
======= RESTART: F:/2018-09勤益科大數值分析/數值分析/PYTHON/EX4-1-0.py ===========
answer = {  1.719713}

exp(x) 在[0, 1]的定積分={  1.718282}

誤差值={  0.001432}

>>>