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

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SUMMARY

The integral of 1/(1-sinx) exists in the range of 0 to 180 degrees. The function is continuous and differentiable within this interval, allowing for standard integration techniques to be applied. A transformation to 1/(1-cosx) can also be considered, particularly when shifting the angle by 90 degrees. However, the behavior of the function around 0 radians indicates that the integral diverges at that point.

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integral of 1/1-sinx exist in 0-180?
 
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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.
 


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.
 

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