How Do You Integrate sin^2(3x)cos^5(3x) dx Using Substitution?

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Discussion Overview

The discussion revolves around the integration of the function sin²(3x)cos⁵(3x) with respect to x. Participants explore various substitution methods and share their experiences with calculus, particularly focusing on integration techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant presents the integral problem and seeks assistance.
  • Another suggests that an odd number of cosines or sines can be simplified, proposing a substitution of u = sin(x) and du = cos(x)dx.
  • A participant questions the original poster's understanding, implying the problem is basic and suggesting they should be studying more formally.
  • The original poster confirms they are self-studying in 10th grade and expresses gratitude for the help.
  • Several participants share their own experiences with early calculus studies and suggest seeking additional resources or tutoring.
  • One participant emphasizes the importance of learning geometry before advancing in calculus, citing it as a potential stumbling block.
  • Another participant offers a specific book recommendation for geometry, while discussing the costs associated with educational materials.
  • A later reply revisits the integration problem, expressing difficulty due to the trigonometric components and requesting a complete solution for clarity.
  • One participant elaborates on a substitution approach, rewriting the integral in terms of sin(x) and cos(x) to facilitate integration.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to the integration problem, and multiple viewpoints regarding the necessity of foundational knowledge in geometry and algebra are presented.

Contextual Notes

Some participants express concerns about the original poster's understanding of geometry and algebra, suggesting these areas may impact their ability to tackle calculus problems effectively. There is also a discussion about the cost of educational resources, indicating financial constraints may affect access to learning materials.

Who May Find This Useful

Students studying calculus, particularly those self-studying or seeking help with integration techniques, as well as individuals interested in the foundational knowledge necessary for advanced mathematics.

Sir.Aaron
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This is a problem I tried a couple days ago and I got stuck on some parts.Here is the problem

[tex]/int sin^2 3xcos^5 3x dx[/tex]
Can anyone help me out?
 
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ignore the threes.an odd number of cosines or sines is equivalent to one of them and an even number of the other, so this is basically sin^6cos, set u = sin(x), and du = cos(x)dx
 
this is basic by the way. are you studying on your own? are you reading the book? do you have a teacher? this is really a simple one. so somehting is amiss here.
 
Yes I am teaching my self. I am still in 10th grade.Thank you for the help
 
Sir.Aaron said:
Yes I am teaching my self. I am still in 10th grade.Thank you for the help
Oh, I started self-studying calculus when I was in grade 10th, too. :approve:
Good luck, man. :smile:
 
forgive my rudeness, you are way ahead of me at your age.

please take my criticism in the vein of the doctors comment that my wife was in "reasonably good condition for a woman in her early 20's" when she was actually 35!.
 
Maybe you could ask your teacher if he/she could refer you to a college or something so you could study there (just being there on their courses).
I started Calc. at 8th grade and was tutored along with college students at a nearby college (or university, as it is called in Sweden where I live)
 
myspip said:
Maybe you could ask your teacher if he/she could refer you to a college or something so you could study there (just being there on their courses).
I started Calc. at 8th grade and was tutored along with college students at a nearby college (or university, as it is called in Sweden where I live)
Thats what I want to do but my problem is I don't know Geometry. I don't understand why I can't understand it. This summer I learned Trig(I bought trig for dummies,awsome book) and started on Calculus. I am currently on integration by parts. I also love physics.
 
the best book i know of on geometry is Geometry, by harold jacobs. i highly recommend it and learning geometry before going to college (or pursuing calculus much further).

hows your algebra? thts the main stumbling block for college calculus.

but in my opinion, a very harmful trend these days is teaching kids calculus befiore they learn algebra and geometry.
 
  • #10
mathwonk said:
the best book i know of on geometry is Geometry, by harold jacobs. i highly recommend it and learning geometry before going to college (or pursuing calculus much further).

hows your algebra? thts the main stumbling block for college calculus.

but in my opinion, a very harmful trend these days is teaching kids calculus befiore they learn algebra and geometry.
Ya that's what I did I made the mistake of learning trig and calculus. I am supposed to be taking a test tomarrow, if I pass this test and another one I get moved into the 12th grade math class. Thanks for the Book recomendation but its $67.00, and for a out of work 10th grader that's a bit steep,lol. My fear is there will be a lot geometry on the tests and that going to make me fail the tests.
 
  • #11
Geometry (ISBN: 0716704560)
Harold R. Jacobs
Bookseller: Great Buy Books
(Lakewood, WA, U.S.A.) Price: US$ 13.23
[Convert Currency] Shipping within U.S.A.:
US$ 3.75
[Rates & Speeds]
Book Description: W.H. Freeman & Company, 1974. Hardcover. Book Condition: GOOD. Dust Jacket Condition: ACCEPTABLE. USED Ships Within 24 Hours - Satisfaction Guaranteed!. Bookseller Inventory # 2762629
 
  • #12
hehe lol. only 3,75 dollars?
My books cost up to 100 dollars each (college math books, last for 2 month).
Well, sometimes you have to invest money on your education (not saying that you should put all your money on it, but a bit maybe). Also, try asking some college students if you can buy their books (second-hand that is)
 
  • #13
Sorry to bring this old topic back, but I can't seem so figure this problem out. Its cause of the trig in the problem. So can someone do the whole problem so I can see how to do it?
 
  • #14
Following mathwonk, we note that cos^2(x) = 1 - sin^2(x), so that cos^4(x) = (1 - sin^2(x))^2. Hence

sin^2(x)cos^5(x) =
sin^2(x)(1 - sin^2(x))^2 * cos(x)

Now make the substitution u = sin(x).
 

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