How to find dx when given transformation?

Question

Can someone please explain to me how to do question 20? Thanks!

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Answer 1 · 2018-06-01T11:09:17

See below

#int_(-3)^0 \ y' \ dx' #

#= int_(+3)^0 3y + 5 \ (-dx) #

#= int_(bb 0)^(bb 3) 3y + 5 \ bb (dx) #

#= 3 int_(0)^3 y \ dx + int_0^3 5 \ dx #

#= 3 (5) + (5x)_0^3 = 30 #