# Evaluate the following quantities using each of the given methods: (a) Use an adaptive quadrature…

Evaluate the following quantities using each of the given methods:

(a) Use an adaptive quadrature routine to evaluate each of the integrals

for k = 0, 1, . . . , 20.

(b) Verify that the integrals just defined satisfy the recurrence

and use it to generate the same quantities, starting with I0 = 1 − e −1 .

(c) Generate the same quantities using the backward recurrence

beginning with In = 0 for some chosen value n > 20. Experiment with different values of n to see the effect on the accuracy of the values generated.

(d) Compare the three methods with respect to accuracy, stability, and execution time. Can you explain these results?

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