from math import exp
def f(x):
    return((x + 2) * exp(-x))

def aireGRNab(N = 6, a = 0, b = 2):
    import matplotlib.pyplot as plt
    pas = (b - a) / N
    tupleX = tuple(a + pas * i for i in range(N + 1))
    tupleY = tuple(f(i) for i in tupleX)
    airetotGran = 0
    plt.figure()
    plt.plot(tupleX, tupleY, 'r-')
    for i in range(N):
        plt.fill((tupleX[i], tupleX[i], tupleX[i + 1], tupleX[i + 1]), (0, tupleY[i], tupleY[i], 0),
                 alpha = 0.5, fill = False, hatch = '//', color = 'green')
        airetotGran = airetotGran + (pas * tupleY[i])
    plt.title('Aire grands rectangles = ' + str(round(airetotGran, 4)))
    plt.xlabel('X')
    plt.ylabel('f(X)')
    plt.axis('equal')
    plt.grid()
    plt.show()