Just because you are calculating a triple integral, it doesn't mean you are calculating a volume. If the integrand was ##1##, you would be, and your method would be correct. But your integrand is ##x^2e^y##, and ##e^y## is not symmetric about ##y=0##. So you don't get the same answer for each quadrant.namehere said:
namehere said:
Yes, that's correct.Eclair_de_XII said:
Quadrant 1 represents the positive x and y values on a coordinate plane. Multiplying the volume by 4 in this quadrant would result in a volume that is too large, as it would include values from all four quadrants. This is incorrect because the problem specifies that the volume should only include values from the first quadrant.
Yes, specifying Quadrant 1 narrows down the range of values that should be included in the volume calculation. This helps to avoid including values from other quadrants and ensures that the calculated volume is accurate for the given problem.
No, because the problem explicitly states that the volume should only include values from Quadrant 1. Multiplying by 4 would include values from all four quadrants, making the solution incorrect.
The correct way to calculate Quadrant 1 Vol x 4 for Problem #13 would be to first find the volume of Quadrant 1, and then multiply that value by 4. This ensures that only values from Quadrant 1 are included in the calculation.
Another common error is forgetting to account for the negative values in Quadrant 1. It is important to remember that Quadrant 1 also includes negative y values, so these should also be included in the volume calculation.