Area between inverse functions

[AlexSendler100%]

Hello fellows can someone please tell me if my calculations here is correct did i got the right value of the are between two inverse functions?

 

[Dr.Peterson]

Hello fellows can someone please tell me if my calculations here is correct did i got the right value of the are between two inverse functions?

The numerical value is approximately correct; but this area is far easier to find if you integrate with respect to y. I get [imath]1 + \sqrt{2}[/imath].