Use python (with libraries) to solve this question.

4. Another approximation for integrals is the Trapezoid Rule: ix co) +2f(x1) + 2f (22) +...+2f(xn-2) + 2f (xn-1) + f(xn) 2 There is a built-in function trapz in the package scipy.integrate (refer to the Overview for importing and using this and the next command). (a) Compute the Trapezoid approximation using n= 100 subintervals. (b) Is the Trapezoid approximation equal to the average of the Left and Right Endpoint approximations? (c) Run the following code to illustrate the trapezoid method with 4 trapezoids (make sure you imported sympy as sp as stated in the Overview): x=sp.symbols('x') f=sp.exp(x/2)/x**3 sp.plot(f,(x,1,5)) xp={1,2,3,4,5) yp=[f.subs({x:i}) for i in xp] import matplotlib.pyplot as plt plt.plot(xp,yp) Notice that the trapezoid approximation is obtained by using lines to estimate f(1) on each subinterval. 4. Another approximation for integrals is the Trapezoid Rule: ix co) +2f(x1) + 2f (22) +...+2f(xn-2) + 2f (xn-1) + f(xn) 2 There is a built-in function trapz in the package scipy.integrate (refer to the Overview for importing and using this and the next command). (a) Compute the Trapezoid approximation using n= 100 subintervals. (b) Is the Trapezoid approximation equal to the average of the Left and Right Endpoint approximations? (c) Run the following code to illustrate the trapezoid method with 4 trapezoids (make sure you imported sympy as sp as stated in the Overview): x=sp.symbols('x') f=sp.exp(x/2)/x**3 sp.plot(f,(x,1,5)) xp={1,2,3,4,5) yp=[f.subs({x:i}) for i in xp] import matplotlib.pyplot as plt plt.plot(xp,yp) Notice that the trapezoid approximation is obtained by using lines to estimate f(1) on each subinterval