Re: Integrate 5.0
- To: mathgroup at smc.vnet.net
- Subject: [mg44251] Re: Integrate 5.0
- From: lalu_bhatt at yahoo.com (Bhuvanesh)
- Date: Fri, 31 Oct 2003 03:01:21 -0500 (EST)
- References: <bnnvfj$61s$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Selwyn Hollis <sh2.7183 at misspelled.erthlink.net> wrote: > I've come to the conclusion that Integrate has become nearly worthless > for computing definite integrals with symbolic limits. To cite a simple > example, > > Integrate[Sqrt[Cos[t] + 1], {t, 0, x}] > > returns an awful mess inside of an If statement (very mild in this > case) that no one should have to deal with if they're only concerned > with real numbers (specifically calculus students and a great many > applied mathematicians). > > On the other hand, DSolve gives the simple, clean answer that Integrate > used to give: > > y[t]/. DSolve[{y'[t] == Sqrt[Cos[t] + 1], y[0] == 0}, y[t], t] > > 2*Sqrt[1 + Cos[t]]*Tan[t/2] > > Could it be that we need a new function such as this: > > RealIntegral[expr_,{x_,a_,b_}]:= > (y[x]/. First@DSolve[{y'[x] ==expr, y[a] == 0}, y[t], t])/.x->b > > that would be associated with \[Integral] ? ... leaving the current > Integrate to be associated with \[ContourIntegral]?? > > Or perhaps a simple option for Integrate like RealLimits->True? > > ----- > Selwyn Hollis > http://www.math.armstrong.edu/faculty/hollis Hi Selwyn, You could specify the assumption that all variables in the limits of integration are real: In[1]:= Integrate[Sqrt[Cos[t] + 1], {t, 0, x}, Assumptions -> x \[Element] Reals] //InputForm Out[1]//InputForm= If[x <= Pi && Pi + x >= 0, 2*Sqrt[1 + Cos[x]]*Tan[x/2], Integrate[Sqrt[1 + Cos[t]], {t, 0, x}, Assumptions -> x \[Element] Reals && (x > Pi || Pi + x < 0)]] In[2]:= $Version Out[2]= 5.0 for Linux (July 10, 2003) Cheers, Bhuvanesh, Wolfram Research. ----- Disclaimer: All opinions expressed are my own and do not necessarily reflect those of Wolfram Research.