python SciPy包计算积分|Python技能树征题

# 答案区
from scipy import integrate
def f(x):
    return x+1

v,err = integrate.quad(f,1,2)
print(v)  #err为误差项

# 数学验证
def F(x):
    return 0.5*x**2+x
print(F(2)-F(1))

输出结果
2.5

# 答案区
from scipy import integrate
def f(x):
    return x**2+2*x+1

v,err = integrate.quad(f,1,2)
print(v)  #err为误差项

# 验证
def F(x):
    return (1/3)*x**3+x**2+x
print(F(2)-F(1))

输出结果
6.333333333333334
6.333333333333333

# 答案区
import math
from scipy import integrate
def f(x):
    return math.sin(x)-math.cos(x)

v,err = integrate.quad(f,0,math.pi)
print(v)


# 验证
def F(x):
    return -math.cos(x)-math.sin(x)
print(F(math.pi)-F(0))

输出结果
1.9999999999999998
2.0

from scipy import integrate
def f(x, a, b):
    return a * x + b
v, err = integrate.quad(f, 1, 2, args = (-1, 1))
print (v)

# 验证
def F(x,a,b):
    return 0.5*a*x**2+b*x
print(F(2,-1,1)-F(1,-1,1))

输出结果
-0.5
-0.5

# 答案区
from scipy import integrate
import numpy as np
def f(x):
    return 1 / np.sqrt(abs(x))
v, err = integrate.quad(f, -1, 1,points=[0])
print (v)

输出结果
3.9999999999999813

from scipy import integrate
import numpy as np
def f(x):
    return np.sqrt(x)
x = np.linspace(0, 2, 10) # np.linspace主要用来创建等差数列
y = f(x)
v = integrate.trapz(y, x)
print (v)

输出结果
1.8652953655957172

# dblquad函数的第一个形参应是f(x,y)、第2、3、4、5分别是a、b、g(x)、h(x),也就是说dblquad函数的第4和5是一个函数
from scipy import integrate
import numpy as np
def f(x, y):
    return x * y
def h(x):
    return x
v, err = integrate.dblquad(f, 1, 2, lambda x: 1, h)
print (v)

输出结果
1.125