Evaluate∫ ∫ f(x,y) dx dy = ?

Question

-Outer integral is from 0 to 5.

-Inner integral is from 2 to 3.

Evaluate Given the following :

f(x,y) = g'(x)y

g(0)=17

g(11)=1

g(2)=1

g(3)=7

g(5)=-12

g(6)=-4

Possible Answers:

a)90, b)-12 , c)75 , d) Can't be done with given information , e)-7 , f) None of these

Answer 1

∫ ∫ f(x,y) dx dy = ∫ ∫ g'(x)*y dx dy = ∫ ∫³₂ g'(x)*y dx dy

∫ ∫³₂ g'(x)*y dx dy = ∫ y*(g(3)-g(2)) dy = ∫ y*(g(3)-g(2)) dy = ∫⁵₀ 6*y dy = (3x²) |₀⁵ = 75