Difficult Trigo Integration, with surd.

  • Context: Undergrad 
  • Thread starter Thread starter wlooi
  • Start date Start date
  • Tags Tags
    Integration
Click For Summary
SUMMARY

The integral ∫sin x√(1+cos2x) dx can be solved using the substitution method. By letting u=cos x, the differential du becomes -sin x dx, simplifying the integral significantly. This approach allows for a second substitution to be applied, facilitating the integration process. The discussion emphasizes the effectiveness of substitution in tackling complex trigonometric integrals.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly integration.
  • Familiarity with trigonometric identities and functions.
  • Knowledge of substitution methods in integration.
  • Experience with manipulating algebraic expressions involving square roots.
NEXT STEPS
  • Practice solving integrals using substitution techniques.
  • Explore advanced trigonometric identities for integration.
  • Learn about integration by parts for more complex integrals.
  • Study the application of definite integrals in real-world problems.
USEFUL FOR

Students and educators in calculus, mathematicians focusing on integration techniques, and anyone seeking to enhance their problem-solving skills in trigonometric integrals.

wlooi
Messages
7
Reaction score
0
∫sin x√(1+cos2x) dx

This question have bugged me for 2 days. Need help please..
 
Physics news on Phys.org
Have you tried letting u=cosx, du=-sinxdx?
You're then left with something that you can yet use another substitution on.
Let's see what you can get.
 

Similar threads

High School ##\int_a^b x^2\sin(2x)dx## by substitution
  • · Replies 2 ·
Replies
2
Views
2K
High School Integration by parts of inverse sine, a solved exercise, some doubts...
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Solving the Difficult Integral ##\int_0^{\infty} x^{n+1} e^{-x} \sin(ax) dx##
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Integration with different infinitesimal intervals
  • · Replies 31 ·
2
Replies
31
Views
5K
High School Question about the limits of integration in a change of variables
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Impossible Integration involving cosx/sqrt(a-bcosx)
  • · Replies 4 ·
Replies
4
Views
2K
High School Straightforward integration…
  • · Replies 27 ·
Replies
27
Views
3K
Undergrad Substitution in a definite integral
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Find ##\int_0^π \sin^ n x dx ##
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad Did Math DF's integral calculator make a glaring mistake?
  • · Replies 8 ·
Replies
8
Views
4K