Answer to Question #162055 in Calculus for Phyroe

Question #162055

Evaluate the integral of (e^-x+e^x)² dx from 0 to 1


1
Expert's answer
2021-02-24T14:17:50-0500

Solution.

01(ex+ex)2dx=01(e2x+2exex+e2x)dx==(12e2x+2x+12e2x)01=12e2+2+12e2+1212==12e2+e22+2.\int\limits_0^1 (e^{-x}+e^x)^2dx=\int\limits_0^1(e^{-2x}+2e^{-x}e^x+e^{2x})dx=\newline =(-\frac{1}{2}e^{-2x}+2x+\frac{1}{2}e^{2x})|_0^1=-\frac{1}{2}e^{-2}+2+\frac{1}{2}e^2+\frac{1}{2} -\frac{1}{2}=\newline =-\frac{1}{2e^2}+\frac{e^2}{2}+2.

Answer. 12e2+e22+2.-\frac{1}{2e^2}+\frac{e^2}{2}+2.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment