How to determine if the formula of my shape is correct? (the formula is found through integration)
For example, I have a pyramid with a rectangle base. The base is represented by 2b by b and the height of the pyramid is h. Pretend that I do not know the correct formula to this question (didn't Google it or didn't ask anyone), am I able to check my formula?
For example, I have a pyramid with a rectangle base. The base is represented by 2b by b and the height of the pyramid is h. Pretend that I do not know the correct formula to this question (didn't Google it or didn't ask anyone), am I able to check my formula?
Checking a formula arrived at by integration seems to required a method that you trust as much as or more than integration.
I'm not sure what method that might be.
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To determine if the formula of your shape is correct when found through integration, you can follow these steps:

Verify the boundaries of integration: Ensure that the limits of integration correspond to the boundaries of the shape you are trying to find the formula for.

Check the integrand: Make sure that the function being integrated represents the quantity you want to find for the shape, such as area, volume, etc.

Evaluate the integral: Perform the integration correctly using appropriate integration techniques. Doublecheck calculations for accuracy.

Compare with known formulas: If possible, compare the resulting formula obtained through integration with known formulas for similar shapes. This can help verify its correctness.

Test against known properties: Test the formula against known properties of the shape, such as symmetry, relationships between dimensions, or known results for specific cases.

Validate with examples: Apply the formula to example cases where the shape's properties are known or can be easily verified. Ensure that the calculated values match expected results.

Seek peer review: If available, seek feedback from peers, instructors, or professionals in the field to validate the correctness of the formula.
By following these steps, you can determine if the formula of your shape, obtained through integration, is correct.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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