Which of the following is  a valid double integral? Group of answer choices∫05∫3𝑦𝑒3𝑥𝑑𝑦𝑑𝑥∫0𝑥∫324𝑥𝑑𝑥𝑑𝑦∫04∫33𝑥𝑒3𝑦𝑑𝑥𝑑𝑦∫01∫3𝑒𝑦4𝑥𝑑𝑥𝑑𝑦 PreviousNext

The valid double integral from the given options is ∫0^1∫3𝑒^𝑦4𝑥𝑑𝑥𝑑𝑦.

Here's why:

1. ∫0^5∫3𝑦𝑒^3𝑥𝑑𝑦𝑑𝑥: This is not valid because the limits of the inner integral are not constants, but a variable (y). The limits of integration for the inner integral should be constants.

2. ∫0^𝑥∫324𝑥𝑑𝑥𝑑𝑦: This is not valid because the limits of the outer integral are not constants, but a variable (x). The limits of integration for the outer integral should be constants.

3. ∫0^4∫33𝑥𝑒^3𝑦𝑑𝑥𝑑𝑦: This is not valid because the limits of the inner integral are not constants, but a variable (x). The limits of integration for the inner integral should be constants.

4. ∫0^1∫3𝑒^𝑦4𝑥𝑑𝑥𝑑𝑦: This is valid because the limits of both the inner and outer integrals are constants.