Integrating cos^3(x) and √cos^3(x): Step-by-Step Guide | Helpful Tips

  • Thread starter Thread starter Player_13
  • Start date Start date
  • Tags Tags
    Integration
Click For Summary

Homework Help Overview

The discussion revolves around integrating the functions cos^(3/2)(x) and √(cos^3(x)). Participants explore various methods and express uncertainty regarding the complexity of these integrals, particularly in the context of an AP calculus problem.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Some participants discuss breaking down cos^3(x) into cos^2(x)cos(x) and using substitutions, while others express confusion about the impact of the square root on the integration process. There are mentions of elliptic functions and their relevance to the problem, with questions about whether the integral can be solved using standard techniques.

Discussion Status

The conversation reflects a mix of attempts to clarify the problem and explore potential methods for integration. Some participants suggest that the integral may not be solvable using elementary functions, while others are seeking confirmation on the requirements for the AP exam regarding showing work and understanding the grading system.

Contextual Notes

Participants note that the problem is derived from a practice AP calculus booklet, raising questions about the expectations for solving such integrals at a high school level. There is also discussion about the implications of negative values in the context of the integrals being evaluated.

  • #31
Player_13 said:
X-43D, I don't think that's correct. I plugged a value for each in my calculator, and the answers were different.

How much did you get?
 
Physics news on Phys.org
  • #32
Yeah I've been playing with it, can't really get anywhere. I was tryin to figure out a way with trig identities to simplify it, but I can't get rid of the square root.
 
  • #33
So I walk into class and my teacher begins to explain the problem... And all she has on the overhead is how to set up the problem, then tells us that she pluged it into the calculator. I guess there is no simple way of solving this, sorry for "wasting" your time with this.
 
  • #34
It's quite likely that it is impossible to find this antiderivative (the EllipticF function most likely can't be expressed in terms of simple functions, although I'm not entirely certain about that)~
 

Similar threads

Understanding a math step in solving Schrödinger's equation for single particle in a box
  • · Replies 8 ·
Replies
8
Views
1K
Is the line integral of tangential force in pendulum equal to the negative of change in potential energy?
  • · Replies 3 ·
Replies
3
Views
1K
Help Calculating probability between 2 limits for the ground state
  • · Replies 28 ·
Replies
28
Views
2K
Line Integral to Verify the Magnetic Field B
  • · Replies 10 ·
Replies
10
Views
2K
Estimating damped harmonic oscillator parameters from this plot of the oscillations
  • · Replies 9 ·
Replies
9
Views
2K
Find the electric field on the surface of a sphere using Coulomb's law
  • · Replies 6 ·
Replies
6
Views
2K
Maximum range on ground for an elevated cannon
  • · Replies 21 ·
Replies
21
Views
4K
Projectile Motion -- Help please understanding these basic problems
  • · Replies 4 ·
Replies
4
Views
2K
Simple Harmonic Motion in x direction
  • · Replies 10 ·
Replies
10
Views
2K
Tension in a string holding a spinning object
  • · Replies 3 ·
Replies
3
Views
2K