Question

If the order of integration of ∫

0
1
​
∫
0
r
2

​
f(x,y)dxdy is reversed as ∫
9
1
​
(x,y)
Q
1
​
(x
1
​
y)
​
∫
h(x,y)
k(x,y)
​
f(x,y) dydx and if then f(4,1)= F(x,y)=g
1
​
(x,y)+g
2
​
(x,y)+n
1
​
{x,y)+n
2
​
(x
1
​
y)
r
​

Answer 1

Reversing the order of integration of a double integral involves switching the limits of integration and the order in which the integrals are evaluated.

The given double integral is:

∫₀¹ ∫₀² f(x,y) dy dx.

When we reverse the order of integration, the new double integral becomes:

∫₁⁹ ∫ᵧ¹ f(x,y) dx dy.

Here, ₁(