from negative infinity to infinity (1/ 4x^2 + 4x +5) dx
is there a way to simplify with partial fracitons or should i do something else? thanks for the help.
this is a question about a steam engine with the equation (sorry for lack of proper math language)
PV^1.4 = k (constant)
using the idea of integral from V1 to V2
ie...
the amount of work done is W=(int.V1 to V2) PdV
Where P1=160lbs/in^2
and V1 = 100 in^3...V2=800 in^3...
1/15*x^15 +1/3*x^12 + 2/3*x^9 + 2/3*x^6 + 1/3*x^3 is the value i got from maple
1/15 (1+x^3)^5 is the value i got by hand...
plug in values of x...u get different results...
if x=1...
the first one u get 31/15...the second is 32/15
integration by parts??
just trying to figure out this integral int(x^2 (1+x^3)^4 dx)
when i integrate by substitution i get anti deriv... 1/15 (1+x^3)^5
which is not the same (but close when u plug in values of x) to
1/15*x^15 +1/3*x^12 + 2/3*x^9 + 2/3*x^6 + 1/3*x^3
am i going about...
take the anti derivative of (X^2)/sqrt(1-x)
soln'... let u=1-x... then -du=dx and x^2 = (1-u)^2 (sub back in)...
this gives me -2*u^(1/2)*(15-10*u+3*u^2) /15... (sorry for lack of proper terms)
anyway, this turns out to be wrong...where did i go wrong here?
If an group G is isomorphic to a group G(prime) then they are only equal or approximately equal. If this can continue on, i.e. G(prime) is isomorphic to a group W... then we are not sure if G is the origional group. Is it possible to find a group that is an origional isomorphism? Does this...
so i actually left this question for a bit. This is my soln' so far...
to show it is an automorphism the groups must be one to one and onto (easy to show) and to show that the function is map preserving I'm saying that for any a and b in Z(n) you will have
(alpha)(a+b) = (alpha)(a) +...
this is what I'm saying so far
since everyelement in G is mapped to it's inverse, and since the following is true alpha(ab)-->(ab)^-1 --->(ba)^-1-->alpha(ba) then G must be abelian for this to be true. ...make sense or am i missing something?