I don't think so. The usual approach is integration by parts, twice. Here's a link to a similar example, https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintsoldirectory/TrigIntSol3.html#SOLUTION 24, problem #24Vitani11 said:Homework Statement
I need to find the coefficients for a Fourier expansion. Here is the integral I need to solve: (1/π) ∫sin(x/2)sin(nx)dx where the limits are from -π to π. The original function for the expansion is f(x) = sin(x/2)
Homework Equations
None
The Attempt at a Solution
Should I do this in terms of complex numbers?
Vitani11 said:I think that should be my approach but I am not sure. If this is the right approach can you help me get started with setting up the integral?
Integration is a mathematical process that involves finding the area under a curve in a given interval. It is the inverse operation of differentiation and is commonly used in calculus to solve various problems in physics, engineering, and other fields.
The limits of integration are determined by the given interval in which the function is to be integrated. These limits represent the starting and ending points of the interval and are denoted by lower and upper bounds respectively.
There are several methods of integration, including substitution, integration by parts, partial fractions, and trigonometric substitution. Each method is used for different types of functions and can be chosen based on the complexity of the given function.
Yes, integration is a powerful tool that can be used to solve real-world problems in various fields such as physics, engineering, economics, and statistics. It is commonly used to find the area under a curve, calculate volumes of objects, and determine the rate of change of a variable.
Some common mistakes to avoid when integrating a function include forgetting to add the constant of integration, misapplying the chain rule, and making errors in algebraic manipulations. It is important to carefully check each step of the integration process to avoid these mistakes.