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Unformatted text preview: use power rule image depends on parameter T  let it go to infinity
 original integral is equal to 1/2 if one diverges, altogether the area is infinite function defined for integral  is continuous infinite area (looking at the
function of
1/x^p shifted
( a constant) when less than one we know
everything
about this
integral not of the form int2 to 5(dx/(x2)^2)
this integral converges  the exponent p is 1/2 which is less than
one from E to 5, the function is defined trying to determine behaviour at
2 function blows up at
x=2 antiderivative
goes to zero is of the form
that we know
about replaced 0 type 2 the exponent is greater than one  this is how we can check
whether our answer is right/wrong
function blows up at x=2  therefore we must isolate this point with the variable E want to
know if
it converges/
diverges
sum of two integrals definite integral if this is shown  it is enough to prove that the
entire integral diverges and therefore has
infinite area split into
two type 2 type 1
converges
when p>1 Type 2 is this integral
divergent/convergent problem at x=0
so we isolate the problem
point integrate by parts if limit is finite number = convergence of the original integral plug in upper and lower limit of integral don't know
the answer
repositioning to be able to use
L'Hopital's rule type 1  infinite interval of integration
bell shape split into two when x goes to + or  infinity,
the function goes to pi/2 ...
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 Winter '07
 MUNTEANU
 Calculus, Power Rule

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