Exercise 1. Use the Maclaurin series of tan-¹(u) tan ¹ (u) =U- to approximate the definite integral with an error of no more than 0.0000001. u³ U² + 3 5 u⁹ + 7 9 7 U 0.1 [0.3+ tan ¹(x²) dx U 11
Exercise 1. Use the Maclaurin series of tan-¹(u) tan ¹ (u) =U- to approximate the definite integral with an error of no more than 0.0000001. u³ U² + 3 5 u⁹ + 7 9 7 U 0.1 [0.3+ tan ¹(x²) dx U 11
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Exercise 1.** Use the Maclaurin series of \(\tan^{-1}(u)\)
\[
\tan^{-1}(u) = u - \frac{u^3}{3} + \frac{u^5}{5} - \frac{u^7}{7} + \frac{u^9}{9} - \frac{u^{11}}{11} + \cdots
\]
to approximate the definite integral
\[
\int_{0}^{0.1} \tan^{-1}(x^2) \, dx
\]
with an error of no more than 0.0000001.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17550e59-88eb-47cf-858a-9b53c1fd9657%2F213a6cd8-9405-43ee-b9fa-72171236a02a%2Fprx62k9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 1.** Use the Maclaurin series of \(\tan^{-1}(u)\)
\[
\tan^{-1}(u) = u - \frac{u^3}{3} + \frac{u^5}{5} - \frac{u^7}{7} + \frac{u^9}{9} - \frac{u^{11}}{11} + \cdots
\]
to approximate the definite integral
\[
\int_{0}^{0.1} \tan^{-1}(x^2) \, dx
\]
with an error of no more than 0.0000001.
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At the end how did you solve the sum to get that result?
I see you replace the x with 0.1 in the last step and I understand that the rest becomes zero when solving th integral, but what did you replace n with to solve the sum?
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