Integral of e^x*sqrt(1 - e^(2x)) using Trigonometric Substitution

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Integral of e^x*sqrt(1 - e^(2x)) using Trigonometric Substitution
  1. The Math Sorcerer
  2. Integration By Substitution
  3. Trigonometric Substitution
  4. Exponential Function
  5. integral
  6. integrate
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Комментарии
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This problem covered a lot of calculus i've learned, Very cool problem!

NaftaliSpodek
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Dear Math Sorcerer,

Was just wondering: after using power reduction angle identity to convert cos^2x into 1/2 +1/2cos2x why do we have to use double angle identity to change the "pesky" 1/2 cos2x into 2sinxcosx before plugging in values from triangle for our final solution?

Can we not plug in values from triangle and just multiply by two?

Btw your exercises are awesome and very helpful, thank you!

AmirJacob_
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Thanks for the solution. I made y=e^x and the problem simplified to int(sqrt(1-y^2))dy and got the same result.

cesarvillegas
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0:50 - how did you differentiate that? implicit differentiation? i'm confused. wouldn't you need to differentiate both sides with respect to theta, giving:
d (e^x) / dθ = cos(θ)
d e^x = cos(θ)dθ
my answer doesn't really make sense to myself, i'm just so confused

tb
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Why didn't you substitute the dx?

josemanuelsanchezmunoz
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But what if you have a 5 instead of the 1???

leahrussinko
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How e^2x=(e^x)^2 ?
Can any one help plz

VaibhaviPhadtare-dspl
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How is e^x = sinø or even u=asinø?? You lost me there.

menzihxni