Clarifying the Use of C1 in Step 3: Solution to Homework Problem

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SUMMARY

The discussion clarifies the use of the constant C1 in the context of solving a specific homework problem involving integration. The equation presented is √3/2 sec θ − 1/2 ln |sec θ + tanθ| + C1, where C1 is defined as −1/2 ln 2 √3. The relationship between C and C1 is emphasized as arbitrary, indicating that either constant can be used interchangeably without affecting the solution's validity.

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Students studying calculus, particularly those tackling integration problems involving trigonometric functions and logarithms.

camboguy
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Homework Statement



MathProblemhelp.jpg


Hello, this is the solution to a problem that i am doing and the only thing i am confused about is why the
C1 in the third step is = to − 1/2 ln 2 √3 as stated in the last line.
=√3/2 sec θ − 1/2 ln |sec θ + tanθ| + C1

that is all i am confused about but i get the rest.

i appreciate the Help Thank you very much.
 
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Subtract the last equation from the next to last to solve for C in terms of C1. Not that the relation between them matters very much. Either one is an arbitrary constant.
 

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