4.24.1_question_3

# make the n divisions for a=0 b=1 n=8
[jtanner@jtw530 ~]$ python -c 'import numpy as np; print([x*.125 for x in range(0,9)])'
[0.0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1.0]

# find f(x) for each division
[jtanner@jtw530 ~]$ python -c 'import numpy as np; print([np.exp(x*.125) for x in range(0,9)])'
[1.0, 1.1331484530668263, 1.2840254166877414, 1.4549914146182013, 1.6487212707001282, 1.8682459574322223, 2.117000016612675, 2.398875293967098, 2.718281828459045]

# add all the f(x) values
[jtanner@jtw530 ~]$ python -c 'import numpy as np; print(sum([np.exp(x*.125) for x in range(0,9)]))'
15.623289651543937

# multiply the sum of f(x)'s by dx
[jtanner@jtw530 ~]$ python -c 'import numpy as np; print(sum([np.exp(x*.125) for x in range(0,9)]) * .125)'
1.952911206442992