# Lecture7 - use power rule image depends on parameter T let...

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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/(x-2)^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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Lecture7 - use power rule image depends on parameter T let...

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