Evaluate the following integrals. int_{-2}^2frac{e^{z/2}}{e^{z/2}+1}dz

naivlingr 2021-01-08 Answered
Evaluate the following integrals.
22ez/2ez/2+1dz
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Expert Answer

Alix Ortiz
Answered 2021-01-09 Author has 109 answers
To Determine: evaluate the following integral .include absolute values only when needed.
Given: we have an integral 22ez/2ez/2+1dz
Explanation: we have22ez/2ez/2+1dz
let us consider 
u=ez/2+1
then
du=12ez/2dz
2du=ez/2dz
the limits also get changed 
z=2 then u=e2/2+1 =e1+1 =1e+1
z=2 then u=e2/2+1 =e1+1
so our integral becomes
22ez/2ez/2+1dz=1e+1e+12udu
=2[ln|u|]1e+1e+1
=2[ln(e+1)ln(1e+1)]
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