# HP 50g calculator's answer is correct or author's answer is correct?

• WMDhamnekar
In summary, we need to evaluate the double integral ##\iint\limits_R e^{\frac{x-y}{x+y}} dA##, where ##R## is the region bounded by ##x \geq 0##, ##y \geq 0##, and ##x+y \leq 1##. The author's answer of ##\frac{e^2 -1}{4e} =0.587600596824## is incorrect because the limits of integration given are for the wrong region. The correct answer, obtained after more than 11 minutes, is ##1.11888345561##.
WMDhamnekar
MHB
Summary: Evaluate ##\displaystyle\iint\limits_R e^{\frac{x-y}{x+y}} dA ## where ##R {(x,y): x \geq 0, y \geq 0, x+y \leq 1}##

Author has given the answer to this question as ## \frac{e^2 -1}{4e} =0.587600596824 ## But hp 50g pc emulator gave the answer after more than 11 minutes of time 1.11888345561.

Now, How to decide which answer is correct?

Your limits of integration are wrong on the inner integral. The integral you entered into the simulator has the region R being ##\{(x, y) | 0 \le x \le 1, 0 \le y \le 1 \}##. IOW, the square bounded by the lines x = 0, y = 0, x = 1, and y = 1. This is incorrect, since the region of integration is a triangle.

Integrating with respect to y first, your integral should look like this:
$$\int_{x=0}^1\int_{y=0}^{1 - x} e^{\frac{x-y}{x+y}}dy dx$$

Orodruin, WMDhamnekar and berkeman

## 1. How do I know if the HP 50g calculator's answer is correct or if the author's answer is correct?

It ultimately depends on the specific problem and the accuracy of the inputs used. However, you can check the calculations manually or use a different calculator to compare the results.

## 2. Can I trust the HP 50g calculator's answer to be accurate?

Yes, the HP 50g calculator is a reliable and accurate scientific calculator. It has been extensively tested and verified by experts in the field.

## 3. What factors can affect the accuracy of the HP 50g calculator's answer?

The accuracy of the HP 50g calculator's answer can be affected by user error, incorrect inputs, and the complexity of the problem. It is important to double-check all inputs and ensure they are entered correctly to get an accurate answer.

## 4. How do I troubleshoot if the HP 50g calculator's answer is incorrect?

If you believe the HP 50g calculator's answer is incorrect, you can try recalculating the problem with different inputs or using a different calculator to compare the results. You can also consult the user manual or online resources for troubleshooting tips.

## 5. Is the author's answer always correct if it differs from the HP 50g calculator's answer?

Not necessarily. The author's answer may be correct, but it is important to consider the accuracy of the inputs and the complexity of the problem. It is always a good idea to double-check and verify the answer using other methods.

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