Final answer:
To evaluate the given double integral, the process involves integrating with respect to x from 0 to cos^{-1}(y) and then integrating the result with respect to y from 0 to 1.
Step-by-step explanation:
To evaluate the double integral ∫01∫0cos-1(y)sin(x)/(1+sin2(x)) dx dy, we need to integrate in two steps. We first integrate with respect to x, and then with respect to y. Starting with the inner integral, we integrate sin(x)/(1+sin2(x)) from 0 to cos-1(y), which may require substitution to simplify the integration process.
Next, after finding the antiderivative in terms of x, we then integrate with respect to y from 0 to 1. It's crucial to remember that proper evaluation of the integral may involve trigonometric identities or substitution methods to simplify the expressions for integration.