Final answer:
The first step in solving an integral using a substitution for x in terms of θ is to identify the appropriate substitution, which simplifies the integral. Subsequently, convert dx to dθ, perform the integral, and check if the solution is reasonable.
Step-by-step explanation:
The first step in solving an integral using a substitution for x in terms of θ is to identify the substitution for x in terms of θ. This involves looking for an expression that can simplify the integral when we substitute it in place of x. After identifying this substitution, the next steps would include evaluating dx in terms of θ and dθ, simplifying expressions, and finally calculating the integral in terms of θ. Once the integral is solved, we substitute θ back into terms of x to obtain the solution in the original variable's terms.
It is crucial to substitute known values along with their units into the appropriate equation to get numerical solutions with units, ensuring the usage of radians for angles where necessary. Finally, it is important to check if the answer is reasonable and makes sense within the context of the problem.