Improper+Integrals+(BC)

==Improper Integrals are a special type of anti derivative in which the limits include an infinity, it can also be defined as the limit of a definite integral at the limits approaches a real number,∞ or −∞, or in some cases as endpoints approach limits. Improper Integrals can not be computed by using normal Riemann sums. For example. T his means that we will have to integrate over an unbounded time interval. To take care of this problem, we will integrate over some finite interval and then consider what happens as ** b ** becomes very large. In particular, ==



this limit may exist in which case we say that the integral // converges // . However, the limit may not exist and we then say that the integral // diverges . //
==Lets take it step by step. To evaluate a definite integral, we anti derive, then we can substitute the two limits into the equation individually, and subtract the numbers they each work out to, for example.==

or

number (ex. //x//=1,000,000,000), this allows the function to level out and get very close to the number it would be
==when //x//=infinity, to the point where the margin or error is negligible. Also as a side note if infinity is your upper limit you would use positive infinity and a positive //x// when you substitute, if infinity is your lower limit however, you would use negative infinity and a negative //x// when you substitute. You may need a calculator to do this substitution but in some cases it is not necessary for example if you have a situation where the function is say ,==

==we know that the anti derivative is X^-1 and and we know that, now if x is in the denominator and x is going to be always increasing, we can substitute it for a very large number (100,000 in this case)==

[[image:kwcalculus/improper_9.gif]]
==This is an important example which illustrates the property of convergence. If the exponent is positive(when p is less than 1), the integral will diverge, while at the same time, if the exponent ends up negative (which is the case when p is greater than 1)the integral converges .==

Sources- http://tutorial.math.lamar.edu/Classes/CalcII/ImproperIntegrals.aspx http://archives.math.utk.edu/visual.calculus/4/improper.1/ http://www.wolframalpha.com/