My text book uses absolute values in the answers for the derivative and integral of arcsec[x], but you don . Why?
calc101.com makes the valid assumption that variables are in domains that allow absolute values to be ignored. This keeps the work simpler. This assumption is legitimate, according to Remark 1, p. 239, Calculus and Analytic Geometry, Fourth Edition, by George B. Thomas Jr., published by Addison-Wesley, 1968. We won’t go into the details here. Essentially the idea is to define the principal values of these functions for negative values of x to be in appropriate intervals. By the way, the functions arccsc[x] and arcsech[x] are similar to arcsec[x]. Of course, none of this matters if x is positive.
calc101.com makes the valid assumption that variables are in domains that allow absolute values to be ignored. This keeps the work simpler. This assumption is legitimate, according to Remark 1, p. 239, Calculus and Analytic Geometry, Fourth Edition, by George B. Thomas Jr., published by Addison-Wesley, 1968. We won’t go into the details here. Essentially the idea is to define the principal values of these functions for negative values of x to be in appropriate intervals. By the way, the functions arccsc[x] and arcsech[x] are similar to arcsec[x]. Of course, none of this matters if x is positive.
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