Question

Change the order of integration: ∫₁³∫₂-xˣ f(x, y) d y d x.

Answer 1

To change the order of integration in the given double integral, rewrite the limits of integration and switch the order of integration.

Step-by-step explanation:

To change the order of integration in the given double integral, we need to rewrite the limits of integration and switch the order of integration. The original integral is ∫₁³∫₂-xˣ f(x, y) d y d x.

Step 1: Rewrite the limits of integration:

The lower limit of the inner integral is 2-xˣ. The upper limit of the inner integral is x = 3. The lower limit of the outer integral is y = 1. The upper limit of the outer integral is y = 3.

Step 2: Switch the order of integration:

The new integral is ∫₂¹ ∫ₓ³ f(x, y) d x d y.