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

naivlingr

naivlingr

Answered question

2021-01-08

Evaluate the following integrals.
22ez/2ez/2+1dz

Answer & Explanation

Alix Ortiz

Alix Ortiz

Skilled2021-01-09Added 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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