How to go about integrating this

  • Thread starter Thread starter samjohnny
  • Start date Start date
  • Tags Tags
    Integrating
Click For Summary
The discussion revolves around the challenge of integrating a specific function, with participants unsure whether to use integration by parts or substitution. A suggestion is made to simplify the process by first substituting y = wt, which would create a simpler argument for the cosine function. Following this, another substitution y = 2x is recommended to apply the double angle formula for cosine, thereby simplifying the integrand further. The conversation emphasizes the importance of strategic substitutions in tackling complex integrals. Overall, the integration process can be streamlined through careful substitutions and formula applications.
samjohnny
Messages
83
Reaction score
1

Homework Statement



Attached

The Attempt at a Solution



I'm not sure how to go about integrating this, i.e. integration by parts, substitution etc?

Any ideas?
 

Attachments

  • integral.JPG
    integral.JPG
    2.4 KB · Views: 373
Physics news on Phys.org
samjohnny said:

Homework Statement



Attached

The Attempt at a Solution



I'm not sure how to go about integrating this, i.e. integration by parts, substitution etc?

Any ideas?

Hint: I would probably make it a little easier by making the sub y = wt first to get a simple argument for the cosine. Then sub y = 2x and apply the double angle formula for cosine and simplify the integrand.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Line Integral Solution for Curve γ: Simplifying Substitutions
  • · Replies 6 ·
Replies
6
Views
941
Can I Use Substitution to Prove the Residue Theorem Integral?
  • · Replies 5 ·
Replies
5
Views
1K
Finding the Fourier cosine series for ##f(x)=x^2##
  • · Replies 4 ·
Replies
4
Views
2K
Double Integral of function in region bounded by two circles
  • · Replies 19 ·
Replies
19
Views
2K
Apparently impossible indefinite integral?
  • · Replies 22 ·
Replies
22
Views
2K
Integration over a set in n-dimensional space
  • · Replies 1 ·
Replies
1
Views
2K
Two ways of integration giving different results
  • · Replies 9 ·
Replies
9
Views
2K
Area surface of revolution (rotating this astroid curve around the x-axis)
  • · Replies 2 ·
Replies
2
Views
2K
Integration of acceleration in polar coordinates
  • · Replies 24 ·
Replies
24
Views
3K
Evaluate the definite integral in the given problem
  • · Replies 1 ·
Replies
1
Views
2K