Solve Integration Problem With u-Substitution

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In summary, the conversation involved a person seeking help with integrating using "u-substitution" and their attempt at solving the equation x(x-1)^3. Another person suggested rewriting the equation and foiling out the (x-1)^3 term before integrating. The conversation also touched on integrating Plancks law to show the Stefan-Boltzmann constant.
  • #1
fran1942
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Hello, I am trying to integrate the following using "u-substitution", however I am not getting the correct result. Can someone please advise where I am going wrong.
The following is my attempt:

x(x-1)^3

u = x-1

du/dx = 1
du/1 = dx

x(u)^4 / 4

My final (incorrect) answer.
x(x-1)^4 / 4
 
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  • #2
hello fran1942! :smile:

(try using the X2 button just above the Reply box :wink:)
fran1942 said:
x(u)^4 / 4

no, you must substitute every x …

you can't end up with something that still has an x in it!:wink:​
 
  • #3
You should rewrite the equation. If you foil out the (x-1)3 to x3-3x2+3x-1 then multiply by the x to get x4-3x3+3x2-x I think you will have an easier time integrating and without using a u-sub.
 
  • #4
Don't forget the constant of integration!
 
  • #5
we cannot seem to integrate Plancks law to show that stefans boltzman constant is 5.67x10^-8
 

FAQ: Solve Integration Problem With u-Substitution

What is u-substitution in integration?

U-substitution is a technique used in calculus to simplify integration problems. It involves substituting a new variable, u, for an expression within the integrand, which allows for easier integration.

When should I use u-substitution?

U-substitution is most commonly used when the integrand contains a function and its derivative, or when the integrand contains an expression that can be simplified by substituting a new variable.

How do I choose the variable u in u-substitution?

The variable u should be chosen based on the expression that is being substituted. It is often helpful to choose u as the inner function in a composite function, or to choose u as a part of the integrand that can be simplified.

What is the general process for solving an integration problem with u-substitution?

The general process for solving an integration problem with u-substitution is as follows:

  1. Select a suitable variable u to substitute.
  2. Calculate the derivative du/dx.
  3. Substitute u and du/dx into the integrand, and rewrite the integral in terms of u.
  4. Solve the resulting integral using basic integration techniques.
  5. Substitute back in the original variable x to get the final answer.

Are there any common mistakes to avoid when using u-substitution?

Some common mistakes when using u-substitution include:

  • Forgetting to replace all instances of the original variable with u when rewriting the integral.
  • Choosing u as something that does not appear in the original integral.
  • Misinterpreting the chain rule when calculating du/dx.

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