Integral, from 0 to 1, of dx/root(1-x^2)

  • Thread starter leo255
  • Start date
  • #1
57
2

Homework Statement


[/B]
Integral, from 0 to 1, of dx/root(1-x^2)

Homework Equations


[/B]
d/dx of arcsin = 1/root(1-x^2)

The Attempt at a Solution



Since d/dx of arcsin = 1/root(1-x^2), we have that the integral, from 0 to 1, of dx/root(1-x^2) equals to arcsin, from 0 to 1.

arcsin(1) - arcsin(0) = arcsin(1). I know I'm missing something here. What did I do wrong?
 

Answers and Replies

  • #2
STEMucator
Homework Helper
2,075
140
Nothing is wrong.
 
  • #3
ehild
Homework Helper
15,523
1,901
Since d/dx of arcsin = 1/root(1-x^2), we have that the integral, from 0 to 1, of dx/root(1-x^2) equals to arcsin, from 0 to 1.

arcsin(1) - arcsin(0) = arcsin(1). I know I'm missing something here. What did I do wrong?
What is arcsin(1)?
 
  • Like
Likes leo255
  • #4
57
2
arcsin(1) is pi/2. I asked someone in my class about this, and he said that I should be taking the limit, as b (or whatever other variable) approaches 1, from the left-hand side. Can you guys confirm if this is something that should be done for this problem?
 
  • #5
34,015
5,667
arcsin(1) is pi/2. I asked someone in my class about this, and he said that I should be taking the limit, as b (or whatever other variable) approaches 1, from the left-hand side. Can you guys confirm if this is something that should be done for this problem?
Yes, this should be done. The integrand is undefined at x = 1, so the Fund. Thm. of Calculus doesn't apply. You can get around this by evaluating this limit:
$$\lim_{b \to 1^-}\int_0^b \frac{dx}{\sqrt{1 - x^2}}$$
 
  • Like
Likes leo255

Related Threads on Integral, from 0 to 1, of dx/root(1-x^2)

  • Last Post
Replies
6
Views
6K
Replies
8
Views
2K
Replies
6
Views
10K
  • Last Post
Replies
8
Views
2K
Replies
1
Views
7K
Replies
15
Views
2K
  • Last Post
Replies
14
Views
2K
Replies
7
Views
84K
Top