Approximating definite integrals Use a Taylor

Chapter 8, Problem 37E

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QUESTION:

Approximating definite integrals Use a Taylor series to approximate the following definite integrals. Retain as many terms as needed to ensure the error is less than \(10^{-4}\).

\(\int_{0}^{0.5} \frac{d x}{\sqrt{1+x^{6}}}\)

Questions & Answers

QUESTION:

Approximating definite integrals Use a Taylor series to approximate the following definite integrals. Retain as many terms as needed to ensure the error is less than \(10^{-4}\).

\(\int_{0}^{0.5} \frac{d x}{\sqrt{1+x^{6}}}\)

ANSWER:

Solution 37E

Step 1:

In this problem we need to approximate the definite integral using Taylor series.

The Taylor series approximation of with center 0 is

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