the trapezoidal rule for approximating Definite Integrals

Approximate ${\int }_0^{\frac{1}{2}}\frac{dx}{1+x^2}$ by using five subintervals. \quad Ans. 0.463

表达式产出：

leftPoint = 0
rightPoint = 1 / 2
subIntervalNum = 5
subIntervalLen = '{}/{}'.format(rightPoint - leftPoint, subIntervalNum)

expressionStrList = []
for i in range(subIntervalNum + 1):
    expressionStrList.append('1/(1+({leftPoint} + {subIntervalLen} * {i})^2)'.format(leftPoint=leftPoint, subIntervalLen=subIntervalLen, i=i))
joinedExpressionStr = ' + '.join(expressionStrList)
print(joinedExpressionStr)

print('{subIntervalLen}*(1/2*{joinedExpressionStr}*1/2)'.format(subIntervalLen=subIntervalLen, joinedExpressionStr=joinedExpressionStr))

Approximate ${\int }_0^3\sqrt{1+x^3}dx$ using six subintervals. \quad Ans. $7.39.$

leftPoint = 0
rightPoint = 3
subIntervalNum = 6
subIntervalLen = '{}/{}'.format(rightPoint - leftPoint, subIntervalNum)

expressionStrList = []
for i in range(subIntervalNum + 1):
    expressionStrList.append('sqrt(1+({leftPoint} + {subIntervalLen} * {i})^3)'.format(leftPoint=leftPoint, subIntervalLen=subIntervalLen, i=i))
joinedExpressionStr = ' + '.join(expressionStrList)
print(joinedExpressionStr)

print('{subIntervalLen}*(1/2*{joinedExpressionStr}*1/2)'.format(subIntervalLen=subIntervalLen, joinedExpressionStr=joinedExpressionStr))