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bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{2} \frac{ dx }{ e ^{\pi x} }\]

bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0that e is to the power of \[\pi x\]

bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0any idea? I think i have to separate the fraction so that 1 is in the numerator and then maybe use "u" substitution? to be able to take the antiderivative?

Tolio
 one year ago
Best ResponseYou've already chosen the best response.2don't need to substitute; the integrand is just e^(pi*x) so the antiderivative is \[\frac{ 1 }{ \pi }e^{\pi x}\]

bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0no that wouldn't work because when you find du it equals 0 = (

Tolio
 one year ago
Best ResponseYou've already chosen the best response.2just plug in your limits and your done :)

bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0it says the answer is \[\frac{ 1 }{ \pi } (1e ^{2\pi})\]

bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0can you show me how to do it step by step? in laments terms lol

Tolio
 one year ago
Best ResponseYou've already chosen the best response.2right! take the expression i gave for the antideriv above and evaluate it at 2 and 0 , ie. plug in 2 then plug in 0 and take the difference \[\frac{ 1 }{ \pi }e ^{2 \pi}\frac{ 1 }{ \pi }e ^{2(0)} = \frac{ 1 }{ \pi } \left( e ^{2 \pi }  1\right)\] \[=\frac{ 1 }{ \pi } \left( 1 e ^{2 \pi } \right) \]

Tolio
 one year ago
Best ResponseYou've already chosen the best response.2ur just muliplying thru by 1 as last step to reverse the terms inside the parentheses

bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0oh ok = ) can you show me step by step how you did the antiderivative. I seem to be having trouble = (

Tolio
 one year ago
Best ResponseYou've already chosen the best response.2whenever u hv e to the power of some constant * x then the antiderivative is the same expoential function divided by the constant \[\int\limits_{}^{}e ^{a x}= \frac{ 1 }{ a } e ^{a x } \]

bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0is that a rule? like what you learn from the book or class? I might just have skimmed over it in my notes and forgot = )

Tolio
 one year ago
Best ResponseYou've already chosen the best response.2definitely one of the standard integration rules but not really worth memorizing as u can see it makes intuitive sense: Dx(e^x) = e^x and Dx(e^ax) = ae^ax so when taking antideriv you hv to put in constant in denominator to get back original function. it's all about thinking in reverse :)

bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0sorry one moment trying to make sense of all this lol

bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0ok so i guess where I'm confused is that i thought the antiderivative formula was \[\frac{ n ^{x+1} }{ x+1 }\] Why is it so different with e and ln from other functions?

Tolio
 one year ago
Best ResponseYou've already chosen the best response.2it is confusing; in your defn, n is a variable and x is a constant, x^2 or x^4, etc. in exponential fncs the n would be the constant and x the variable which requires different treatment the following whole webpage is great to explain the derivation but just to understand the difference a little more concretely scroll down to the very bottom of the page :) http://tutorial.math.lamar.edu/Classes/CalcI/DiffExpLogFcns.aspx

Tolio
 one year ago
Best ResponseYou've already chosen the best response.2http://tutorial.math.lamar.edu/Classes/CalcI/ComputingIndefiniteIntegrals.aspx

bettyboop8904
 one year ago
Best ResponseYou've already chosen the best response.0thank you so much this page is helping me out a lot = ) @Tolio
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