Question

(b - y_t / 1-t) dt db_t ; verify y_t = a(1-t)

Answer 1

The question seems to pertain to the verification of a mathematical physics formula, but due to its unclear nature, an exact solution cannot be provided. Instead, a general method to verify an equation using calculus is discussed.

Step-by-step explanation:

The question presented seems to be a mathematical physics problem dealing with an expression involving variables t, d, b, and y_t. The expression provided is unclear and appears to be a differential or integration relating to magnetic fields (e.g., B field) or movement equations over time. Verification of a formula y_t = a(1-t) is also requested in the context. However, due to the ambiguous nature of the question, I will instead provide a step-by-step guide on how to verify an equation using integration and differentiation, using y_t = a(1-t) as an example.

1. Write down the equation you need to verify: y_t = a(1-t).
2. If the equation involves differentiation or integration, apply the corresponding mathematical operation. For differentiation, you would take the derivative with respect to t, and for integration, you would integrate with respect to t within the limits provided.
3. After performing the mathematical operation, compare the result with the provided or known form to confirm if the verification holds true.

In this case, without clear expression to work with or instructions on the operation to be applied, we cannot perform the verification process accurately.