Integrating by Parts: Solving ∫r^3/(4+r^2)^(1/2) dr

  • Thread starter Thread starter AnnieF
  • Start date Start date
  • Tags Tags
    Integrating parts
Click For Summary
SUMMARY

The integral ∫r^3/(4+r^2)^(1/2) dr can be effectively solved using a substitution method rather than integration by parts. The recommended substitution is u = r^2 + 4, which simplifies the integral significantly. Participants in the discussion confirmed that using this substitution leads to a more straightforward solution compared to the initial attempts with integration by parts. This approach allows for easier manipulation of the integral and avoids unnecessary complications.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with integration techniques, specifically integration by parts
  • Knowledge of substitution methods in integration
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Practice solving integrals using substitution methods
  • Review the integration by parts formula ∫udv=uv-∫vdu
  • Explore advanced techniques in integral calculus, such as trigonometric substitutions
  • Study examples of integrals that require both substitution and integration by parts
USEFUL FOR

Students studying calculus, educators teaching integration techniques, and anyone looking to improve their problem-solving skills in integral calculus.

AnnieF
Messages
13
Reaction score
0

Homework Statement



∫r^3/(4+r^2)^(1/2) dr

Homework Equations



∫udv=uv-∫vdu

The Attempt at a Solution



I know that integration by parts must be used. I tried doing it with 4+r^2 as u, but kept running into issues..then I got an answer but it appears to be wrong. I guess I am not sure how to do this.
 
Physics news on Phys.org
First substitute r^2=t, then integrate by parts.ehild
 
I don't think it needs integration by parts. I'd do a simple u substitution. u=r^2+4, like AnnieF suggested. What 'issues' were you running into?
 
Dick said:
I don't think it needs integration by parts. I'd do a simple u substitution. u=r^2+4, like AnnieF suggested. What 'issues' were you running into?

The substitution u=r^2 would be significantly easier to deal with. One can then use parts or another substitution to make the integral elementary.
 

Similar threads

Surface Integral of a sphere
  • · Replies 9 ·
Replies
9
Views
1K
Symmetry of an Integral of a Dot product
  • · Replies 9 ·
Replies
9
Views
2K
Why Does My Integration Over a Sphere Give Incorrect Results?
  • · Replies 2 ·
Replies
2
Views
2K
The volume of a "spherical cap" using triple integrals
  • · Replies 9 ·
Replies
9
Views
2K
Using the Divergence Theorem on the surface of a sphere
  • · Replies 5 ·
Replies
5
Views
3K
Surface Area of a Sphere in Spherical Coordinates
  • · Replies 14 ·
Replies
14
Views
2K
Schwarzschild coordinate time integral
  • · Replies 3 ·
Replies
3
Views
1K
Setting the limits of an integral
  • · Replies 3 ·
Replies
3
Views
2K
Integral of f(x): Get Answer Here
  • · Replies 13 ·
Replies
13
Views
2K
Calculate this Integral around the Circular Path using Green's Theorem
  • · Replies 3 ·
Replies
3
Views
2K