Integral of 1/1-sinx exist in 0-180?

  • Thread starter k.a
  • Start date
  • Tags
    Integral
In summary, the integral of 1/1-sinx in the interval 0-180 is ln|secx + tanx| + C, where C is a constant. It exists in the interval 0-180 due to the continuity and well-defined nature of the function. Other methods such as substitution can also be used to solve it. The indefinite integral is also ln|secx + tanx| + C. The interval 0-180 is significant as it represents a half-period of the sine function, but the integral can also be evaluated in multiples of this interval.
  • #1
k.a
1
0
integral of 1/1-sinx exist in 0-180?
 
Physics news on Phys.org
  • #2
Assuming you mean 1/(1-sinx) and the domain is in degrees, the answer is no. It is easier to explain if you shift it 90 degrees and integrate 1/(1-cosx) from -90 to 90. Around 0 (when you use radians rather than degrees), (1-cosx) behaves like x2/2, therefore the integral blows up at this point.
 
  • #3


Yes, the integral of 1/1-sinx does exist in the range of 0-180 degrees. This is because the function 1/1-sinx is continuous and differentiable in this interval, and therefore it can be integrated using standard integration techniques.
 

FAQ: Integral of 1/1-sinx exist in 0-180?

What is the integral of 1/1-sinx in the interval 0-180?

The integral of 1/1-sinx in the interval 0-180 is ln|secx + tanx| + C, where C is a constant.

Why does the integral of 1/1-sinx exist in the interval 0-180?

The integral of 1/1-sinx exists in the interval 0-180 because the function 1/1-sinx is continuous and well-defined in that interval, and the integral of a continuous function exists within a closed interval.

Can the integral of 1/1-sinx be solved using any other method?

Yes, the integral of 1/1-sinx can also be solved using the substitution method, where u = tan(x/2).

What is the indefinite integral of 1/1-sinx?

The indefinite integral of 1/1-sinx is ln|secx + tanx| + C, where C is a constant.

What is the significance of the interval 0-180 in this integral?

The interval 0-180 represents a half-period of the sine function, which is why the integral of 1/1-sinx is typically evaluated within this interval. However, the integral can also be evaluated in multiples of this interval, such as 0-360 or 0-540.

Similar threads

I Why is the absolute value of sinx used in the integral of cotx?
Replies
1
Views
955
Lim x->0: Why Can't I Replace (x-sinx)/(sinx)^3 with 1/(sinx)^2-1/(sinx)^2?
Replies
2
Views
1K
MHB Integral with sinx in the denominator
Replies
2
Views
1K
B Why is the definite integral of 1/x from -1 to 1 undefined?
Replies
4
Views
3K
I Integral Bee Preparation -- Trouble with this beautiful integral
Replies
10
Views
2K
I Integrating 1/x with units (logarithm)
Replies
15
Views
2K
I Integration with different infinitesimal intervals
Replies
31
Views
2K
B Integration by parts of inverse sine, a solved exercise, some doubts...
Replies
4
Views
2K
I Definite integral is undefined and not undefined
Replies
8
Views
1K
B How do physicists know if limits exist, things are integrable, etc?
Replies
12
Views
896

Hot Threads

Recent Insights

Back
Top