How Do You Evaluate the Integral of (x^2 + y^2)^(-3/2) with Respect to y?

  • Context: Undergrad 
  • Thread starter Thread starter crossroads
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary
SUMMARY

The integral of (x^2 + y^2)^(-3/2) with respect to y can be evaluated using trigonometric substitution. The variable x^2 is treated as a constant during the integration process. The correct evaluation leads to the result of -1/y√(x^2 + y^2). Review of trigonometric substitution and integration techniques is essential for mastering this integral.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with trigonometric substitution techniques
  • Knowledge of integration by substitution
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study trigonometric substitution methods in calculus
  • Practice integration by substitution with various functions
  • Review integral calculus concepts from advanced textbooks
  • Explore examples of integrals involving (x^2 + y^2) terms
USEFUL FOR

Students studying calculus, mathematics educators, and anyone looking to improve their skills in evaluating complex integrals.

crossroads
Messages
2
Reaction score
0
I took calc a year ago, and already am apparently rusty. I'm trying to figure out how to evaluate the integral: [tex]\int (x^2+y^2)^(^-^3^/^2) dy[/tex]. This isn't a homework problem by the way, its actually an example problem in the book, but they don't show step by step how they got to the answer. If someone could go through this step by step that would be really nice :). You're just supposed to treat the x^2 as a constant, right? I get as far as: [tex](-2 (x^2+y^2)^(^-^1^/^2^)) / 2y[/tex] but I'm not even sure if that much is correct. Thanks for any help.
 
Last edited:
Physics news on Phys.org
Welcome to PF!

Hi crossroads! Welcome to PF! :smile:

(have an integral: ∫ and a square-root: √ and try using the X2 tag just above the Reply box :wink:)

Yes, x2 is a constant.

No, it isn't -1/y√(x2 + y2).

Hint: try a trig substitution. :wink:​
 
Thanks for the hint and the welcome. I got the answer, but it looks like I need to review my trig substitutions and integration by substitution.
 

Similar threads

Undergrad Integration of ##e^{-x^2}## with respect to ##x##
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad The Euler-Lagrange equation and the Beltrami identity
  • · Replies 1 ·
Replies
1
Views
3K
MHB 15.1.34 Evaluate triple integral
  • · Replies 2 ·
Replies
2
Views
2K
High School Calculating shaded area: I'm getting discrepancies between methods
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Why does the integral of sine of x^2 from - infinity to + infinity diverge?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad How to evaluate the enclosed area of this implicit curve?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad How Do You Integrate 1/√(x^3 + x^2 + x + 1) dx?
  • · Replies 8 ·
Replies
8
Views
2K
MHB How do I evaluate this triple integral for 2ze^(-x^2) over the given bounds?
  • · Replies 6 ·
Replies
6
Views
2K
MHB How Do You Set Up Double Integrals Over a Semicircular Region?
  • · Replies 10 ·
Replies
10
Views
4K