# Integrating (2/a)[200sin(3πx)sin(nπx/a)] from 0 to a

• maherelharake
In summary, the conversation involves a student seeking help with integrating a given equation using a website and manually. The website calculates the result without plugging in the bounds, leading to doubts about its accuracy. The student also attempts to integrate the equation by parts but is unable to get a definite result. They are then advised to use proper delimiters when inputting the equation on the website.
maherelharake

## Homework Statement

I need to integrate

(2/a) [200sin(3*Pi*x)sin(n*pi*x/a)] from 0 to a. In this equation , 'a' is a constant. I don't have to show my work, just the final answer.

## The Attempt at a Solution

I used a website, and got a result which I have attached. This online calculator does not plug in the bounds. However, this doesn't seem correct to me. I tried to integrate it by parts (to check), but couldn't get it to work. Any help? Thanks.

#### Attachments

• int.jpg
3.4 KB · Views: 359
If you only want to find an answer you can use www.wolframalpha.com and tell it:
"integrate f(x) dx from 0 to a"

However, it is always good to know how to do stuff by hand. I think two integrations by parts should work.

integrate (2/a)[200sin(3*Pi*x)sin(n*pi*x/a)dx from 0 to a

I couldn't get it to give me a definite result. It gave me an indefinite result, but I would like to learn how to use this site properly too.

Ohhh ok. Thanks.

## 1. What is the purpose of integrating (2/a)[200sin(3πx)sin(nπx/a)] from 0 to a?

The purpose of integrating this expression is to find the area under the curve represented by the function within the given limits. This area can have physical or mathematical significance depending on the context in which the integration is being performed.

## 2. How do you solve the integration of (2/a)[200sin(3πx)sin(nπx/a)] from 0 to a?

The integration can be solved using various integration techniques, such as trigonometric substitution or integration by parts. It is important to carefully apply the chosen method and use appropriate algebraic manipulations to arrive at the final solution.

## 3. What is the value of n in the given expression?

The value of n can be any integer, as long as it is greater than 1. This is because the given expression involves the product of two sine functions, and the value of n determines the number of oscillations in the second sine function within the interval [0, a].

## 4. How does the value of a affect the result of the integration?

The value of a affects the result of the integration as it determines the limits of integration. A larger value of a will result in a larger interval and thus, a larger area under the curve. Additionally, the value of a also affects the frequency of the sine functions within the given expression.

## 5. What are the possible applications of integrating (2/a)[200sin(3πx)sin(nπx/a)] from 0 to a?

The integration can have various applications in fields such as physics, engineering, and mathematics. For example, it can be used to calculate the work done by a varying force over a certain distance, or to find the total energy of a vibrating system. It can also be used to solve differential equations in physics and engineering problems.

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