Final answer:
Given w as a function of s and t, the question asks for partial derivative ratios. After calculating σw/σt = 2t and σw/σs = 3s^2, their reciprocals are found to answer the question.
Step-by-step explanation:
The question presents an equation w = ∫(s3 + t2 ) where w is a function of s and t, and asks us to find σt / σw and σs /σw. It appears there is an error in the symbols used, as σ typically represents the standard deviation in statistics, but in the context of calculus, it could refer to partial derivatives. Assuming this is the case, we can denote the partial derivative with respect to a variable as a subscript of w (for example, ws for ∂w/∂s). The partial derivatives of w would be σw/σt = 2t and σw/σs = 3s^2, indicating the rate of change of w with respect to each variable. The reciprocals of these would give us the desired quantities.