Expand Integrand: Understand Int'l Calculus Concepts

  • Thread starter jwxie
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In summary, the conversation discusses the process of expanding an integrand and solving a specific integral by setting a substitution and using the formula for integrating a polynomial. The goal is to get a polynomial plus a constant of integration, which can then be simplified and solved further. The concept of expanding an integrand is used to simplify and solve more complex integrals.
  • #1
jwxie
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Is this an expand integrand?
[tex]\int 9x[/tex] [tex]^{2}[/tex] [tex]/[/tex] (3 - x)[tex]^{4}[/tex]

I set u = ( 3 - x)
du = -1dx

and so if i treat x = 3 - u , i might get this integral

[tex]\int[/tex] 9(3-u)[tex]^{2}[/tex] (u)[tex]^{4}[/tex]

the answer is
(3[tex]/[/tex]x - 1) [tex]^{-3}[/tex] + c
but i can't get it...

Originally, from the book, it gave a simple example like this

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

then
negative [tex]\int[/tex] [tex](2-u) [/tex] u[tex]^{1/2}[/tex]

it sets
u = 2 - x
du = -dx
and x = 2-u

I just don't get what EXPANDED INTEGRAND is really doing...
 
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  • #2
Hi jwxie! :smile:

(have an integral: ∫ and try using the X2 tag just above the Reply box :wink:)

"expand the integrand" simply means multiply it out, so that you get a/u4 + b/u3 + c/u2, and then integrate that

and after you've done that, you should get a polynomial plus a constant of integration … then you can subtract a multiple of u3/u3 from the constant, and complete the cube :wink:
 

Related to Expand Integrand: Understand Int'l Calculus Concepts

What is the purpose of expanding the integrand in international calculus?

The purpose of expanding the integrand is to simplify the integral and make it easier to solve. By breaking down the integrand into smaller, more manageable parts, it becomes easier to manipulate and integrate.

What are some common techniques used to expand the integrand?

Some common techniques used to expand the integrand include using algebraic identities, trigonometric identities, and integration by parts. These techniques can help to simplify the integrand and make the integral easier to solve.

How does expanding the integrand relate to international calculus concepts?

Expanding the integrand is an important concept in international calculus because it allows for the evaluation of more complex integrals. By understanding how to expand the integrand, one can better understand the concepts of integration and apply them to various international calculus problems.

What are some challenges that may arise when expanding the integrand?

Some challenges that may arise when expanding the integrand include identifying the appropriate techniques to use, knowing when to stop expanding, and keeping track of the various parts of the integrand. It is important to carefully work through each step and check for errors along the way.

How can I practice and improve my skills in expanding the integrand?

One way to practice and improve your skills in expanding the integrand is to work through various examples and exercises. There are also many online resources and textbooks available that provide practice problems and solutions. Additionally, seeking help from a tutor or instructor can also be beneficial in improving your skills.

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