Simple single variable integral calc

In summary, a simple single variable integral is a mathematical concept used to find the area under a curve on a graph. To solve it, you need to identify the function and limits of integration and use techniques like substitution or integration by parts. Some applications of single variable integrals include calculating distances, volumes, and areas in various fields. Technology can be used to solve these integrals, but it is important to have a solid understanding of the concepts behind it. Common mistakes when solving these integrals include forgetting rules, making algebraic errors, and improper setup of limits of integration. Regular practice is essential to avoid these mistakes.
  • #1

Homework Statement



e^x dx
1+e^2x

Homework Equations


The Attempt at a Solution



Its the e^x and the e^2x that's tripping me up, i know that e^x is just itself but what is the rule behind e^2x?
 
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  • #2
u = e^x
du= e^xdx

So then your integral is

u/(1+u^2)du

Does that look like something (think arc(something))
 
  • #3
[tex]\int\frac{e^x}{1+e^{2x}}dx[/tex]

[tex]u=e^x[/tex]
[tex]du=e^xdx[/tex]

PowerIso meant ...

[tex]\int\frac{du}{1+u^2}[/tex]
 

1. What is a simple single variable integral?

A simple single variable integral is a mathematical concept that involves finding the area under a curve on a graph. It is a fundamental concept in calculus and is used to solve a variety of problems in physics, engineering, and other fields.

2. How do you solve a simple single variable integral?

To solve a simple single variable integral, you first need to identify the function and the limits of integration. Then, you can use integration techniques such as substitution, integration by parts, or partial fractions to evaluate the integral and find the area under the curve.

3. What are the applications of simple single variable integrals?

Simple single variable integrals have many applications in real-world problems. They are used to calculate distances, volumes, areas, and other physical quantities in fields such as physics, engineering, economics, and statistics.

4. Can you use technology to solve simple single variable integrals?

Yes, there are many software programs and online tools that can help you solve simple single variable integrals. These tools use numerical methods to approximate the integral and provide a solution. However, it is important to understand the concepts and techniques behind integration before relying solely on technology.

5. What are some common mistakes when solving simple single variable integrals?

Some common mistakes when solving simple single variable integrals include forgetting to apply the correct integration rules, making algebraic errors, and not properly setting up the limits of integration. It is important to double-check your work and practice regularly to avoid these mistakes.

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