Trig substitution (integration)

Click For Summary
SUMMARY

The discussion centers on the application of trigonometric substitution in integration, specifically using the secant function for the expression involving the square root of a quadratic. The correct substitution is identified as x = (3/2)sec(θ), which incorporates the necessary coefficient adjustment. Participants confirm the importance of dividing out constants to ensure accurate integration results.

PREREQUISITES
  • Understanding of trigonometric functions, particularly secant
  • Familiarity with integration techniques in calculus
  • Knowledge of algebraic manipulation involving square roots and quadratics
  • Basic skills in substitution methods for integrals
NEXT STEPS
  • Study the method of trigonometric substitution in calculus
  • Learn about the properties and applications of the secant function
  • Practice integration problems involving square roots of quadratics
  • Explore advanced integration techniques, including integration by parts
USEFUL FOR

Students studying calculus, particularly those focusing on integration techniques, as well as educators seeking to enhance their teaching of trigonometric substitution methods.

joess
Messages
16
Reaction score
0

Homework Statement


30x75o8.gif


Homework Equations



The Attempt at a Solution


I'm not asking for someone to do the question for me but I was just wondering what I'm supposed to sub in. Do I put in
2pyuz2w.gif
as if it was (x^2-9)^(1/2) or do I have to do something differently if there is a constant in front of the x^2? Thanks for any help.
 
Physics news on Phys.org
You are correct, secant is the correct trig function to use in this case.
However the coefficient is incomplete, you need to divide out the 4 as well.
 
So is it x=(3/2)sec(theta) ?
 
That's right! :)
 

Similar threads

Using Euler's formula to prove trig identities using "sum to product" technique
  • · Replies 4 ·
Replies
4
Views
2K
How to Prove the Integral of sin^7 x/(1+x^10) dx from -pi/2 to pi/2 is 0?
  • · Replies 14 ·
Replies
14
Views
2K
Indefinite Integral: How to Use Trig Substitution?
  • · Replies 1 ·
Replies
1
Views
1K
Potential of a rotationally symmetric charge distribution
  • · Replies 4 ·
Replies
4
Views
1K
Integral using substitution x = -u
  • · Replies 12 ·
Replies
12
Views
2K
Integration question involving square root
  • · Replies 4 ·
Replies
4
Views
2K
Using hyperbolic substitution to solve an integral
  • · Replies 18 ·
Replies
18
Views
3K
How do I know what to substitute(u-substitution)
  • · Replies 3 ·
Replies
3
Views
2K
How Do You Solve the Integral ∫x/(6x-x^2)^3/2 dx Using Trig Substitution?
  • · Replies 2 ·
Replies
2
Views
1K
Integrating trig powers, why not by parts?
  • · Replies 5 ·
Replies
5
Views
2K