How Does the Substitution Rule Work?

  • Thread starter jkeatin
  • Start date
  • Tags Tags
    Substitution
1 reply · 3K views · last reply
jkeatin
Messages
66
Reaction score
0

Homework Statement


If u=g(x) is a differentiable function whose range is an interval I and f is continuous on I, then Integral f(g(x)g'(x)dx=Integral f(u)du.


Homework Equations





The Attempt at a Solution

 

Discussion

Similar threads

Substitution Rule for Integrals: How to Simplify Complex Integrands
  • Arnoldjavs3
  • · Replies 2 ·
  • Calculus and Beyond Homework Help
Replies
2
Difficulties with Substitution Rule (integration)
  • quicksilver123
  • · Replies 4 ·
  • Calculus and Beyond Homework Help
Replies
4
How does the substitution d(sin 2010x) convert to dx?
  • Delzac
  • · Replies 2 ·
  • Calculus and Beyond Homework Help
Replies
2
What does that substitution do to the integral?What is the resulting integral?
  • ana111790
  • · Replies 2 ·
  • Calculus and Beyond Homework Help
Replies
2
How Does the Substitution x=es, y=et Transform the PDE for f(x,y)?
  • CrimsnDragn
  • · Replies 1 ·
  • Calculus and Beyond Homework Help
Replies
1
Undergrad How does the substitution x = 1/z transform Bessel's Equation?
  • Philip Land
  • · Replies 1 ·
  • Differential Equations
Replies
1
Undergrad Confusion about the Substitution rule
  • JohnnyGui
  • · Replies 28 ·
  • Calculus
Replies
28
Simplifying the Substitution Rule for Integration
  • bobsmith76
  • · Replies 3 ·
  • Calculus and Beyond Homework Help
Replies
3
Undergrad Substitution in a definite integral
  • mcastillo356
  • · Replies 6 ·
  • Calculus
Replies
6
Finding the Value of an Integral with U-Substitution
  • Zack K
  • · Replies 2 ·
  • Calculus and Beyond Homework Help
Replies
2