_-substitution: definite integral of exponential function | AP Calculus AB | Khan Academy

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Finding the definite integral from 0 to 1 of x__2^(x_). Created by Sal Khan.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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Thanks a lot for the video. Just a small remark: you can use U-substitution from the start without incrementing exponential function to the power ==> at the end you will get the same answer.

earthschool

Words cannot do justice to how this calculus series has helped me. Thanks, really thank you. Advice: watch from the website not from YouTube or at least follow the order from the website if you really want to get the most out of this course.

manarsalem

We could have also just called 2^(x^3) = u which would have caused u' / 3*ln(2) = the inside of the integral. Which means we then only need to solve for the definite integral of (2^(x^3)) from 0 to 1

cheat

Thanks for these, I'm getting better and better at calculus with each subsequent Khan Academy calculus tutorial.

putzak

why all this? just set u equal x cubed and then divide be three to get 3x^2dx=du then change the boundaries from 0 and 1 to 0^3 and 1^3 so it stays the same then integrate to get 1/3[2^u/ln2] from 0 to 1 which is 1/3[2/ln2 - 1/ln2] which is 1/3ln2 which simplifies to i dont see the need to make all these complicated substitutions with e and all that extra stuff

Geffosome

Integral of a^u = ((a^u)/ln(a))+C ... No need to complicate things

jpdube

I have learned a lot from that he does. No matter if this is complicated.

AslamSg_pro

Just went over that in my calc class :)

DoomVik

_-substitution: definite integral of exponential function | AP Calculus AB | Khan Academy

_-substitution: definite integral of exponential function | AP Calculus AB | Khan Academy

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