Solving an Integral: Is My Attempt Right?

  • Thread starter Jumpy Lee
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In summary, the best way to check if your attempt at solving an integral is correct is to double-check your work and compare it to a reliable source or use an online integral calculator. Common mistakes to avoid when solving integrals include using incorrect integration rules, not simplifying the integral, and making calculation errors. To improve your skills, it is recommended to practice regularly and seek help when needed. It is possible to solve an integral using multiple methods, such as substitution, integration by parts, and partial fractions. Solving integrals has many real-world applications, including finding area and volume, calculating work, and in various fields of science.
  • #1
Jumpy Lee
20
0

Homework Statement



[tex]\int x/2x-20)^(1/2) [/tex]

The Attempt at a Solution



I did u sub got the [tex]\int (u+20)/(2u^1/2)du [/tex] which became (1/6)(2x-20)^(3/2) + 10(2x-20)^(1/2)

Is this right? What am i doing wrong if it is not.
 
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  • #2
Do you mean
[tex]\int\frac{u+20}{2u^{1/2}}du[/tex]
If so that is the same as
[tex]\int [(1/2)u^{1/2}+ 10u^{-1/2}]du[/tex]
I don't see how you would get 2x-20- since there is no x in the original integral!
 

1. How do I know if my attempt at solving an integral is correct?

The best way to check if your attempt at solving an integral is correct is to double-check your work and compare it to the solution provided in the answer key or by a reliable source. You can also plug your solution into a graphing calculator or online integral calculator to verify the answer.

2. What are some common mistakes to avoid when solving integrals?

Some common mistakes to avoid when solving integrals include forgetting to use the correct integration rules, not simplifying the integral before solving, and making calculation errors. It is also important to pay attention to any constants or variables that may affect the solution.

3. How can I improve my skills in solving integrals?

The best way to improve your skills in solving integrals is to practice regularly and to seek help from a tutor or teacher if you are struggling. You can also watch tutorial videos or attend workshops to learn new strategies and techniques for solving integrals.

4. Is it possible to solve an integral using more than one method?

Yes, it is possible to solve an integral using more than one method. In fact, it is often helpful to use multiple methods to check your work and to gain a better understanding of the integral. Some common methods include substitution, integration by parts, and partial fractions.

5. What are some real-world applications of solving integrals?

Solving integrals has many real-world applications, including calculating the area under a curve, finding the volume of irregular shapes, and determining the work done by a variable force. It is also used in various fields of science, such as physics, engineering, and economics.

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