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

In summary: This becomessin^2(x)cos^5(x) = sin^2(x)cos(u*x) + sin^2(x)cos^5(u*x)and simplifying this, we getsin^2(x)cos^5(x) = sin^2(x)cos(u*x) + cos^2(x)which is the same as the original equation.In summary, this problem involves finding the cosine of a function using substitution. Using basic trigonometry, one can solve for cosine using the equation sin^2(x)cos^
  • #1
Sir.Aaron
13
0
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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  • #2
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
 
  • #3
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.
 
  • #4
Yes I am teaching my self. I am still in 10th grade.Thank you for the help
 
  • #5
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:
 
  • #6
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!.
 
  • #7
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)
 
  • #8
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.
 
  • #9
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).
 

1. How do I approach an integration problem?

The first step in approaching an integration problem is to identify the type of integration problem it is. This can be done by looking at the integrand and the limits of integration. Once you have determined the type of integration problem, you can use the appropriate integration technique, such as substitution or integration by parts.

2. What are some common integration techniques?

Some common integration techniques include substitution, integration by parts, partial fractions, and trigonometric substitution. These techniques can be used to solve a variety of integration problems and it is important to become familiar with them in order to effectively solve integration problems.

3. How do I know if my answer to an integration problem is correct?

One way to check if your answer to an integration problem is correct is to differentiate your answer and see if it gives you the original function. You can also use online integration calculators to check your answer. It is important to double check your work, especially when dealing with more complex integration problems.

4. What are some common mistakes to avoid when solving integration problems?

One common mistake when solving integration problems is forgetting to include the constant of integration. Another mistake is incorrectly applying integration rules, such as the power rule or the chain rule. It is important to be careful and precise when solving integration problems to avoid making these types of mistakes.

5. How can I improve my skills in solving integration problems?

The best way to improve your skills in solving integration problems is through practice. The more you practice, the more familiar you will become with different integration techniques and the easier it will be to approach and solve integration problems. You can also seek out additional resources, such as textbooks or online tutorials, to further improve your understanding and skills in integration.

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