How to integrate ((e^x)-e^(-x)) between 1 and 0?

Question

#int_0^1(e^x-e^-x)dx#

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Answer 1 · 2018-04-21T13:14:45

#I=(e-1)^2/e#

Here,

#I=int_0^1(e^x-e^-x)dx#

#=[e^x]_0^1-[-e^-x]_0^1#

#=[e^1-e^0]+[e^-1-e^0]#

#=e-1+e^-1-1#

#=e+1/e-2#

#=(e^2+1-2e)/e#

#=(e^2-2e+1)/e#

#=(e-1)^2/e#