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

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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.
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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.
 
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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.
 

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.

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