Evaluate the following integral: ∫ln 2 0 ∫ln 5 1 𝒆^(𝟐𝒙+𝒚) 𝒅𝒚𝒅𝒙

Question

the limits of the integrals are ln 2 to 0 and ln 5 to 1

and (2x + y) is to the power of e

Thank you do much if you could answer this :)

Answer 1

∫ln 2 0 ∫ln 5 1 𝒆^(𝟐𝒙+𝒚) 𝒅𝒚𝒅𝒙 = ∫ln 2 0 ∫ln 5 1 𝒆^𝟐xe^𝒚) 𝒅𝒚𝒅𝒙 =∫ln 2 0 e^2x [e^ln5 - e¹] dx =

 

(5-e)•½•[e^2ln2 - e^o] = (5-e)•½•(2² - 1) = (3/2)(5-e).

 

I have assumed that the lower limits were 0 and 1, respectively, on the integrals.  Do you agree with my result?