【scipy】用python的库 scipy 求一重积分 |
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scipy求二重(多重)积分:点击跳转. sympy求积分:点击跳转. 问题1:求解如下一重积分: F ( x ) = ∫ 0 1 x 2 + e x + 1 d x . F(x) = \int_0^1 x^{2}+e^{x}+1 ~dx\,. F(x)=∫01x2+ex+1 dx. 程序1. import scipy.integrate as integrate import numpy as np result = integrate.quad(lambda x: x**2 + np.exp(x) + 1, 0, 1) print(result)程序2. import scipy.integrate as integrate import numpy as np def f(x): return x**2 + np.exp(x) + 1 result = integrate.quad(f, 0, 1) print(result) 结果: (3.051615161792378, 3.3879734149171206e-14)问题2:假设求解如下积分: F ( x ) = ∫ 0 1 a x 2 + b x + c d x . F(x) = \int_0^1 ax^{2}+bx + c~dx\,. F(x)=∫01ax2+bx+c dx. 假设: a = 3 , b = 2 , c = 1 a=3, ~b=2, ~c=1 a=3, b=2, c=1 即: F ( x ) = ∫ 0 1 3 x 2 + 2 x + 1 d x . F(x) = \int_0^1 3x^{2}+2x + 1~dx\,. F(x)=∫013x2+2x+1 dx. 程序: from scipy.integrate import quad def integrand(x, a, b, c): return a*x**2 + b*x + c a = 3 b = 2 c = 1 I = quad(integrand, 0, 1, args=(a,b,c)) print(I) 结果: (3.0, 3.3306690738754696e-14) |
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