Improper Integrals | MIT 18.01SC Single Variable Calculus, Fall 2010

[420headband]

At the end of the video. Why does she not take the -3^(1/3)?

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[LadySaberKnight]

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[miami360x]

I got all 3 right :)

[RAHELL19FM]

if the area in example (a) always cancels out when b--> infinity , why isnt the integral of cos x equal to zero? or is it only zero for values 2*k*pi ( with k : 0 and positive integers)?

[yoyaya007]

@RAHELL19FM because infinity is not defined as 2kpi when k goes to infinity for positive integers. we don t know what is infinity there for we can t say it s 0

[niuchemist]

@RAHELL19FM It's zero for 2kpi, as you mentioned, because the function is periodic, as you know. So for every upward slope, there is a downward slope. The two are equal in area, but opposite about the y axis (and so negative with respect to area). They cancel each other out.

[spychic101]

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