The correct answer is ∫03∫𝑦9𝑓(𝑥,𝑦)𝑑𝑥𝑑𝑦.

Here's why:

The original integral is ∫09∫0𝑥𝑓(𝑥,𝑦)𝑑𝑦𝑑𝑥. This means that y varies from 0 to x, and x varies from 0 to 9.

When we change the order of integration to dx dy, we need to express the limits of x in terms of y.

Looking at the original limits, we can see that x varies from y to 9 (because y goes up to x, and x goes up to 9).

So, the new limits for x are from y to 9. The limits for y remain the same, from 0 to 3.

Therefore, the integral becomes ∫03∫𝑦9𝑓(𝑥,𝑦)𝑑𝑥𝑑𝑦.

Question

The correct answer is ∫03∫𝑦9𝑓(𝑥,𝑦)𝑑𝑥𝑑𝑦.

Here's why:

The original integral is ∫09∫0𝑥𝑓(𝑥,𝑦)𝑑𝑦𝑑𝑥. This means that y varies from 0 to x, and x varies from 0 to 9.

When we change the order of integration to dx dy, we need to express the limits of x in terms of y.

Looking at the original limits, we can see that x varies from y to 9 (because y goes up to x, and x goes up to 9).

So, the new limits for x are from y to 9. The limits for y remain the same, from 0 to 3.

Therefore, the integral becomes ∫03∫𝑦9𝑓(𝑥,𝑦)𝑑𝑥𝑑𝑦.

Knowee AI · Accepted Answer

The correct answer is ∫03∫𝑦9𝑓(𝑥,𝑦)𝑑𝑥𝑑𝑦.

Here's why:

The original integral is ∫09∫0𝑥𝑓(𝑥,𝑦)𝑑𝑦𝑑𝑥. This means that y varies from 0 to x, and x varies from 0 to 9.

When we change the order of integration to dx dy, we need to express the limits of x in terms of y.

Looking at the original limits, we can see that x varies from y to 9 (because y goes up to x, and x goes up to 9).

So, the new limits for x are from y to 9. The limits for y remain the same, from 0 to 3.

Therefore, the integral becomes ∫03∫𝑦9𝑓(𝑥,𝑦)𝑑𝑥𝑑𝑦.

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