Final answer:
The question seeks the values of B₁, H₁, and x₁ for an integration formula, but the provided information isn't sufficient to determine these values without additional context.
Step-by-step explanation:
The question asks us to find the values of B₁, H₁, and x₁ for the approximate integration formula ∫_-1^1 f(x) d x ≈ B₁ f(-1)+H₁ f(x₁).
To do this, we must look at the given equation and determine the coefficients that apply. However, based on the provided information, it seems there's not enough to outright solve for B₁, H₁, and x₁.
The provided information appears to be from various contexts and doesn't directly relate to this question.
Normally, determining these values would require a known integrand or additional conditions such as being part of a certain numerical integration rule (like the trapezoidal rule or Simpson's rule).
In the absence of such guidance, one cannot specifically determine the values of B₁, H₁, and x₁ solely from the information given.