Trouble Understanding Integration Problem | Solutions Manual Confusion

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In summary, a simple integration problem involves finding the area under a curve by integrating a function and is a fundamental concept in calculus. To solve it, one must identify the function and limits of integration, use integration rules and techniques to find the antiderivative, and evaluate the integral. Common techniques include the power rule, substitution, integration by parts, and trigonometric substitutions. While calculators can be used, it is important to understand the concepts and techniques behind integration. Real-world applications include calculating displacement, finding volume, and solving problems in economics, physics, and engineering.
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jofree87
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I am having a trouble understanding why the solutions manual is using u-substitution here. Am I forgetting a rule or something?

I don't know how to post in the correct notation so I'll post pictures instead.

I am suppose to integrate equation (4) in the picture. The solutions manual shows equation (6) as their answer. The answer I got is this:

= 1/2*RAx2 - woL/4(x2/2 - Lx/3) + C3

I believe they are using u-substitution for the (x-L/3). Am I doing something wrong?
 

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The answer you give and the answer they give differ only by a constant. So both answers are correct.
 

1. What is a "Simple Integration Problem"?

A simple integration problem is a mathematical problem that involves finding the area under a curve by integrating a function. It is a fundamental concept in calculus and is used to solve a variety of real-world problems.

2. How do I solve a simple integration problem?

To solve a simple integration problem, you first need to identify the function and limits of integration. Then, use integration rules and techniques to find the antiderivative of the function. Finally, plug in the limits of integration and evaluate the integral.

3. What are some common techniques used to solve simple integration problems?

Some common techniques used to solve simple integration problems include the power rule, substitution, integration by parts, and trigonometric substitutions. It is important to practice and understand these techniques to solve integration problems efficiently.

4. Can I use a calculator to solve a simple integration problem?

Yes, you can use a graphing calculator or a computer program to solve simple integration problems. However, it is important to understand the concepts and techniques behind integration to use these tools effectively.

5. What are some real-world applications of simple integration problems?

Simple integration problems have many real-world applications, such as finding the area under a velocity-time graph to calculate displacement, finding the volume of irregular objects, and calculating the work done by a variable force. They are also used in economics, physics, and engineering to model and solve various problems.

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