Which of the following is a valid double integral? Group of answer choices∫05∫3𝑦𝑒3𝑥𝑑𝑦𝑑𝑥∫0𝑥∫324𝑥𝑑𝑥𝑑𝑦∫04∫33𝑥𝑒3𝑦𝑑𝑥𝑑𝑦∫01∫3𝑒𝑦4𝑥𝑑𝑥𝑑𝑦 PreviousNext
Question
Which of the following is a valid double integral? Group of answer choices∫05∫3𝑦𝑒3𝑥𝑑𝑦𝑑𝑥∫0𝑥∫324𝑥𝑑𝑥𝑑𝑦∫04∫33𝑥𝑒3𝑦𝑑𝑥𝑑𝑦∫01∫3𝑒𝑦4𝑥𝑑𝑥𝑑𝑦 PreviousNext
Solution
The valid double integral from the given options is ∫0^1∫3𝑒^𝑦4𝑥𝑑𝑥𝑑𝑦.
Here's why:
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∫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.
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∫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.
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∫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.
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∫0^1∫3𝑒^𝑦4𝑥𝑑𝑥𝑑𝑦: This is valid because the limits of both the inner and outer integrals are constants.
Similar Questions
Which of the following is a double integral evaluated on a region bounded by the curves 𝑥2+4𝑦2=4 and 𝑥+2𝑦=2 in the first quadrant? Group of answer choices∫01∫2−2𝑦4−4𝑦2𝑓(𝑥,𝑦)𝑑𝑥𝑑𝑦∫02∫1−𝑥24−𝑥22𝑓(𝑥,𝑦)𝑑𝑦𝑑𝑥None of theseBoth integrals
Double-integral gives
Evaluate the double integral: ∫023∫𝑦/43/21−𝑥2𝑑𝑥𝑑𝑦using change of coordinates. Group of answer choices1/67/62/31/3 PreviousNext
If the order of integration is reversed for the double integral ∫−11∫𝑥21𝑒𝑥+𝑦𝑑𝑦𝑑𝑥, the integral will become _____. Group of answer choices∫02∫−𝑦𝑦𝑒𝑥+𝑦𝑑𝑥𝑑𝑦∫01∫−𝑦𝑦𝑒𝑥+𝑦𝑑𝑥𝑑𝑦None of these∫𝑥21∫−11𝑒𝑥+𝑦𝑑𝑥𝑑𝑦 PreviousNext
To evaluate the double integral ∫01∫3𝑦3𝑒𝑥2𝑑𝑥𝑑𝑦 it is best to:Group of answer choicesnone of the choicesevaluate in the given orderchange coordinateschange the order of integration
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