Is ∫-1/√(1-x^2) equal to acos(x) and -1*asin(x)?

  • Context: Undergrad 
  • Thread starter Thread starter Nikitin
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the relationship between the integral of -1/√(1-x^2) and the inverse trigonometric functions acos(x) and asin(x). Participants explore whether these expressions are equivalent, particularly in the context of integration and the constant of integration.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant asserts that acos(x) equals the integral of -1/√(1-x^2) and questions if this implies that ∫-1/√(1-x^2) also equals -1*asin(x).
  • Another participant references the identity arcsin x + arccos x = π/2 to challenge the initial claim, suggesting a potential error in the reasoning.
  • A participant expresses uncertainty about their previous calculations, indicating they cannot find an error in their reasoning.
  • Another participant suggests that the constant of integration may have been overlooked in the discussion.
  • A later reply acknowledges the oversight regarding the constant of integration, attributing the confusion to recent exam stress.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are competing views regarding the equivalence of the integrals and the implications of the constant of integration.

Contextual Notes

The discussion highlights the importance of the constant of integration in evaluating indefinite integrals, which remains unresolved in the context of the claims made.

Nikitin
Messages
734
Reaction score
27
Since acos(x) = ∫-1/√(1-x^2), and asin(x) = ∫1/√(1-x^2), won't ∫-1/√(1-x^2) = acos(x) = -1*asin(x)?
 
Physics news on Phys.org
arcsin x + arccos x = pi/2

so I think what you have is wrong, check again.
 
I doublechecked, but I still can't find my error..
 
Nikitin, is there any chance that you are forgetting the constant of integration?
 
oops, yeh, true :p

sorry, I had a brainfart due to 3 weeks of exams
 

Similar threads

Undergrad ##f(2x)=f^2(x)-2f(x)-1/2## then find ##f(3)##
  • · Replies 17 ·
Replies
17
Views
4K
Undergrad Why are the accelerations not equal?
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Question about Limit: \lim_{x\rightarrow1} (x+1)
  • · Replies 29 ·
Replies
29
Views
3K
Undergrad Find ##\int_0^π \sin^ n x dx ##
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad Integration of √(1-x^2) with x=sinθ: Check Correctness and Simplification
  • · Replies 12 ·
Replies
12
Views
3K
MHB Crank/Piston Motion: Understanding dB/dt, dB/dθ & d2B/dT2
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Verifying Integration of ##\int_0^1 x^m \ln x \, \mathrm{d}x##
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Area of a Circle: Solving the Equation
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Partial derivative interpretation
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Significance of (1+1/x)^x as x->-inf
  • · Replies 6 ·
Replies
6
Views
2K