How do you integrate (r^2-x^2)^(1/2) with a constant r?

  • Thread starter Thread starter FUNKER
  • Start date Start date
  • Tags Tags
    Integrate
Click For Summary
SUMMARY

The integration of (r^2 - x^2)^(1/2) with a constant r can be effectively solved using trigonometric substitution. Specifically, substituting x with r * sin(u) or r * cos(u) simplifies the integral significantly. This method leverages the Pythagorean identity to facilitate the integration process, leading to a straightforward solution. The discussion confirms that trigonometric substitution is a reliable technique for this type of integral.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with trigonometric identities
  • Knowledge of trigonometric substitution techniques
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study trigonometric substitution methods in calculus
  • Practice integrating functions involving square roots
  • Explore the Pythagorean identity and its applications in integration
  • Learn about other substitution techniques for integrals
USEFUL FOR

Students and professionals in mathematics, particularly those focusing on calculus and integration techniques, will benefit from this discussion.

FUNKER
Messages
120
Reaction score
0
how would you integrate
(r^2-x^2)^(1/2)
where r is constant
thanks peace
 
Mathematics news on Phys.org
i think it's pretty straightforward with trig substitution. try replacing x with cos(u), sin(u) or tan(u) or something like that & the solution should drop out.
 

Similar threads

Undergrad Why does the integral of sine of x^2 from - infinity to + infinity diverge?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Area of a Circle: Solving the Equation
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Challenging integral involving exponentials and logarithms
  • · Replies 14 ·
Replies
14
Views
3K
High School Is it possible to find the integral of ##f(x)/x^2##?
  • · Replies 8 ·
Replies
8
Views
2K
MHB Find Analytic Expression for Integral with Approximations
  • · Replies 1 ·
Replies
1
Views
1K
MHB Solving $\tan^2x + \tan^2{2x} + \cot^2{3x} = 1$ in R
  • · Replies 6 ·
Replies
6
Views
1K
Graduate How Does U(1) Double-Cover SO(2) for a Specified Angle?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Why Does the Polar Moment of Inertia Use r^2 in Its Formula?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Determine ## \beta ## as a function of ##\theta## linkage
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Solving Stat Mech Integral with Wolfram Alpha
  • · Replies 2 ·
Replies
2
Views
2K