Have a question about integrals

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In summary, the conversation revolved around finding the integral of (tan4x)^2 using different methods, such as the box method and the integral by parts method. The conversation ended with the poster providing their solution and offering to share it with others.
  • #1
kevinf
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Homework Statement



integrate (tan4x)^2.

Homework Equations





The Attempt at a Solution



i have tried the box method but it won't work. i have also been told to do the integral b parts using dv, v, u, and du. i have heard of that method but the teacher insists on teaching the box method. is it possible with the box method.
 
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  • #2
[tex]\int\tan^{2}{4x}dx[/tex]

yes? ima start working on it. idk what the box method is. also, show some work or i won't post anything if i even get anywhere, lol.
 
  • #3
i have tried to convert that to the sin over cos and then integrating but i don't have any idea what to do after that
 
  • #4
dope! trig identity ...
 
  • #5
anybody else got it?? i really just want the steps getting to the answers not necessarily the answer
 
  • #6
Hmmm...remember [tex]sec^2A=1+tan^2A[/tex] so if ever A=4x ...you can replace tan[tex]^2[/tex]4x with sec
 
  • #7
i told you!

[tex]\int\tan^{2}{4x}dx=\int(\sec^{2}4x-1)dx[/tex]
 
  • #8
I'm simply wondering, what is the box method? I never heard of it.
 
  • #9
PowerIso said:
I'm simply wondering, what is the box method? I never heard of it.
maybe it's the table method?
 
  • #10
here is my answer in the file

i have added a file with my solution
 

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  • #11
your picture will have to be approved

just post a link
 
  • #12
where can i upload it or an email adress to send it?

you can also contact me using icq: 466921864

i will send it to you
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value or quantity of something that is constantly changing, such as velocity or volume.

2. How do you solve integrals?

Integrals can be solved using various techniques, such as substitution, integration by parts, or the fundamental theorem of calculus. It is important to first identify the type of integral and then choose the appropriate method to solve it.

3. What are the applications of integrals?

Integrals have various applications in mathematics, physics, engineering, and other fields. They can be used to calculate areas, volumes, work, and other quantities that involve continuous change. They are also used in differential equations, optimization problems, and statistics.

4. What is the difference between definite and indefinite integrals?

A definite integral has specific limits of integration and gives a numerical value as the result. It represents the total change or quantity within a specific range. An indefinite integral has no limits of integration and gives a general function as the result. It represents the antiderivative or reverse process of differentiation.

5. How do integrals relate to derivatives?

Integrals and derivatives are closely related as they are inverse operations of each other. The derivative of a function gives the rate of change at a specific point, while the integral of a function gives the total change or quantity over a range. The fundamental theorem of calculus connects these two operations and allows for the evaluation of integrals using derivatives.

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