Explain to me the integration techniques?

In summary, the conversation discusses the topic of integration techniques and the possibility of a shortcut for simplifying integrals. It also mentions the need for practice problems with answers for related rates.
  • #1
okkvlt
53
0
Can somebody explain to me the integration techniques?

Also, say you have something like
x^8*5*2
so do i really need to simplify the integral 8 times just to get rid of the x^8 term? Is there a shortcut?

Also, i need some related rates practice problems. With answers so i can check myself.
 
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  • #2
okkvlt said:
Can somebody explain to me the integration techniques?
Is not uncommon for an entire semester course to be devoted to that!

Also, say you have something like
x^8*5*2
so do i really need to simplify the integral 8 times just to get rid of the x^8 term? Is there a shortcut?
What do you mean by "x^8*5*2"? If you mean (x^8)*5*2 that is just 10x^8 which has anti-derivative (10/9)x^9+ C. If you mean x^(8*5*2) that is just x^(160) which has anti-derivative (1/161)x^(161)+ C. I don't know what you mean by "simplify the integral 8 times".

Also, i need some related rates practice problems. With answers so i can check myself.
Get a good calculus book.
 
  • #3
I got careless. By x^8*5*2 i actually meant x^8 times 5^x
 

1. What is integration and why is it important?

Integration is the process of finding the area under a curve or the sum of infinitely small parts. It is important because it allows us to solve a wide range of problems in mathematics, science, and engineering.

2. What are the different techniques for integration?

There are several techniques for integration, including the use of basic integration rules, substitution, integration by parts, partial fractions, and trigonometric substitution.

3. How do I know which integration technique to use?

The choice of integration technique depends on the form of the integrand. You can start by using basic integration rules and then move on to more complex techniques if needed. Practice and experience will also help you determine which technique to use.

4. Can integration techniques be used for both definite and indefinite integrals?

Yes, integration techniques can be used for both definite and indefinite integrals. For definite integrals, the result is a numerical value, while for indefinite integrals, the result is a function.

5. Are there any tips for solving integration problems?

Yes, here are a few tips for solving integration problems: 1) Always check the limits of integration; 2) Use algebraic manipulation to simplify the integrand; 3) Look for patterns or relationships between the integrand and known functions; 4) Practice and familiarize yourself with common integration techniques.

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