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find the integral between ln π/2 and π/6 2e^u du ? 

 May 2, 2020
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Compute the definite integral:
 integral_log(π/2)^(π/6) 2 e^u du

Factor out constants:
 = 2 integral_log(π/2)^(π/6) e^u du

Apply the fundamental theorem of calculus.
The antiderivative of e^u is e^u:
 = 2 e^u right bracketing bar _log(π/2)^(π/6)

Evaluate the antiderivative at the limits and subtract.
 2 e^u right bracketing bar _log(π/2)^(π/6) = 2 e^(π/6) - 2 e^log(π/2) = 2 e^(π/6) - π:
 
= 2 e^(π/6) - π  - Courtesy of Mathematica 11 Home Edition.

 May 2, 2020

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