How Do You Integrate 59x(cos(x))^2?

  • Thread starter Mugen Prospec
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In summary, the conversation is about solving the integral \int 59x(cos(x))^2 dx. The student attempted to use integration by parts but got stuck. Another user suggested using the identity \cos^2(x) = \frac {1 + \cos{(2x)}}{2} and integrating by parts again. The student is unsure of the next step and asks for clarification.
  • #1
Mugen Prospec
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Homework Statement



[tex]\int[/tex] 59x(cos(x))2 dx


Homework Equations





The Attempt at a Solution



I tried doing integration by parts with u= (cos(x))2 and dv= xdx
v= [tex]\frac{x^2}{2}[/tex]
However this didnt get me very far can some one tell me what the first step or two are.
 
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  • #2
I got the the answer to be 59([tex]\frac{1}{4}[/tex]x sin(2x) + [tex]\frac{1}{8}[/tex]cos(2x) + [tex]\frac{x^2}{4}[/tex])
But this was from my calculator I still don't know how to do it.
 
  • #3
Use:

[tex]\cos^2(x) = \frac {1 + \cos{(2x)}}{2}[/tex]

and integration by parts.
 
  • #4
ok Ill check it out thanks
 
  • #5
OK I tried it and it just got more complicated. Whats the next step?
 
  • #6
what LCKurtz suggested shoudl lead to a pretty simple integral, maybe show what you did
 
  • #7
just did x(1+co(2x)/(2))
Do i distribute or use by parts now?
 
  • #8
yep multiply out and use parts on the (x.cos(2x)) part
 

FAQ: How Do You Integrate 59x(cos(x))^2?

What is the purpose of "Integrating 59x(cos(x))^2: A Step-by-Step Guide"?

The purpose of this guide is to provide a step-by-step process for integrating the function 59x(cos(x))^2. This function is commonly used in mathematics and physics, and understanding how to integrate it is important in solving many problems in these fields.

What is the formula for integrating 59x(cos(x))^2?

The formula for integrating 59x(cos(x))^2 is: ∫ 59x(cos(x))^2 dx = 59x(1/2 sin(2x) + 1/4 x) + C

How do you solve for the integration of 59x(cos(x))^2?

To solve for the integration of 59x(cos(x))^2, you need to use the power reduction formula for cosine: cos^2x = (1/2)(1+cos2x). Then, you can use the substitution method or integration by parts to evaluate the integral.

Are there any tips for solving the integration of 59x(cos(x))^2?

One tip for solving the integration of 59x(cos(x))^2 is to carefully follow the steps in the guide and double check your work. It is also helpful to practice with similar integrals to improve your understanding and technique.

What are some real-life applications of integrating 59x(cos(x))^2?

Integrating 59x(cos(x))^2 is used in many real-life applications, such as calculating the work done in a physics problem involving a moving object with changing acceleration. It is also used in determining the power output in an electrical circuit and in modeling the growth of certain populations in biology.

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