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

In summary, the conversation is about using the Maclaurin series for sin(7x^2) to evaluate an integral and estimating its value using the first two terms. The user made an error in their attempt which was corrected by another user.
  • #1
HolyDesperado
16
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
  • #2
You forgot powering the 7, you need 7^(2n+1).
 
  • #3
Thank you, I see my error now and the suggestion lead me to a correct answer.
 

What is a Mac series?

A Mac series, also known as a Maclaurin series, is a representation of a mathematical function as an infinite sum of terms that are calculated from the function's derivatives at a specific point, usually 0.

How is a Mac series used to solve integrals?

A Mac series can be used to approximate the value of an integral by using the known series expansion for a particular function, such as sin(x). By substituting the series into the integral and evaluating the terms, an approximate value can be found.

Why is sin(x) commonly used in Mac series?

Sin(x) is commonly used in Mac series because it has a well-known and simple series expansion. This makes it easier to use for approximating integrals compared to other functions with more complex series expansions.

What is the process for solving integrals using a known Mac series for sin(x)?

The process for solving integrals using a known Mac series for sin(x) involves substituting the series into the integral, evaluating the terms, and then taking the limit as the number of terms approaches infinity to get an approximation for the integral value.

What are the limitations of using Mac series to solve integrals?

Mac series can only be used to approximate the value of an integral and not give an exact solution. Additionally, the series may not converge for all values of x, making it limited in its applicability. Other methods, such as numerical integration, may be more accurate for certain integrals.

Similar threads

Solving a Gaussian integral using a power series?
    • Calculus and Beyond Homework Help
Replies
9
Views
2K
Does the series converge using the integral test?
    • Calculus and Beyond Homework Help
Replies
16
Views
3K
How can I find the limit of the integral?
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
    • Calculus and Beyond Homework Help
Replies
7
Views
706
Calculate integral sin(x)/x^0.1dx from pi to infinity
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Solving Confusing Log Limit
    • Calculus and Beyond Homework Help
Replies
6
Views
1K
Finding the Solution to a Maclaurin Series for Sin(x)
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Using known Maclaurin series to approximate modification of original
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Taylor Series Error Integration
    • Calculus and Beyond Homework Help
Replies
6
Views
3K
Maclaurin Series for f(x)=(1-x)^-2: Find Solution
    • Calculus and Beyond Homework Help
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top