Solving Integrals Using a Known Mac Series (Sin(x))

Click For Summary
SUMMARY

The discussion focuses on evaluating the integral of sin(7x^2) using its Maclaurin series expansion. The user initially miscalculated the series by neglecting to include the factor of 7 raised to the power of (2n+1). After receiving guidance, the user corrected their approach and successfully derived the correct infinite series representation. The importance of accurately applying the Maclaurin series for sin(x) is emphasized in solving integrals involving polynomial transformations.

PREREQUISITES
  • Understanding of Maclaurin series expansions
  • Familiarity with trigonometric functions, specifically sin(x)
  • Knowledge of integral calculus
  • Ability to manipulate infinite series
NEXT STEPS
  • Study the Maclaurin series for other trigonometric functions
  • Learn how to derive and apply Taylor series for polynomial functions
  • Explore techniques for evaluating integrals involving infinite series
  • Investigate error analysis in series approximations
USEFUL FOR

Students and educators in calculus, mathematicians focusing on series expansions, and anyone interested in solving integrals using series methods.

HolyDesperado
Messages
16
Reaction score
0

Homework Statement


Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin(7x^2) to evaluate the integral https://webwork.math.lsu.edu/webwork2_files/tmp/equations/f4/767c0643696d085d77f9a697294a311.png

Your answer will be an infinite series. Use the first two terms to estimate its value.

Homework Equations


Inline44.gif



The Attempt at a Solution


http://img27.imageshack.us/img27/5028/mathhelp2k.jpg

After the final step in the picture, I plugged in n=0 and 1 to get my 0th and 1st terms, then I added them together and I got: 0.754110411. This is wrong, however.. can someone please help me diagnose this problem?
 
Last edited by a moderator:
Physics news on Phys.org
You forgot powering the 7, you need 7^(2n+1).
 
Thank you, I see my error now and the suggestion lead me to a correct answer.
 

Similar threads

Solving a Gaussian integral using a power series?
  • · Replies 9 ·
Replies
9
Views
3K
How can I find the limit of the integral?
  • · Replies 3 ·
Replies
3
Views
2K
Does the series converge using the integral test?
  • · Replies 16 ·
Replies
16
Views
4K
Calculate integral sin(x)/x^0.1dx from pi to infinity
  • · Replies 2 ·
Replies
2
Views
2K
Estimating integral with Maclaurin series
  • · Replies 11 ·
Replies
11
Views
9K
Using known Maclaurin series to approximate modification of original
  • · Replies 3 ·
Replies
3
Views
2K
Finding the Solution to a Maclaurin Series for Sin(x)
  • · Replies 3 ·
Replies
3
Views
1K
Maclaurin Series for f(x)=(1-x)^-2: Find Solution
  • · Replies 7 ·
Replies
7
Views
2K
How Do You Use the Maclaurin Series to Evaluate the Integral of sin(3x^2)?
  • · Replies 1 ·
Replies
1
Views
2K
How Can the Limit of (ln(1+x))^x as x Approaches 0 Be Evaluated Correctly?
  • · Replies 6 ·
Replies
6
Views
2K