Approximate ∫012dx1+x2\int_{0}^\frac{1}{2} \frac{d x}{1+x^{2}}∫0211+x2dx 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 ∫031+x3dx\int_{0}^{3} \sqrt{1+x^{3}} d x∫031+x3dx using six subintervals. \quadAns. 7.39.7.39 .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))