Final answer:
To evaluate the iterated integral, start by evaluating the inner integral with respect to y, and then integrate the result with respect to x. Finally, evaluate the outer integral to get the final answer.
Step-by-step explanation:
To evaluate the given iterated integral ∫ π/2 x ∫ ∫ x sin(y) dy dx0 0, we start by evaluating the inner integral first. The inner integral involves integrating with respect to y, treating x as a constant. The integral of sin(y) with respect to y is -cos(y). So, the inner integral becomes -cos(y) evaluated from 0 to π/2 x.
Next, we integrate the result of the inner integral with respect to x. So, the outer integral becomes ∫ -cos(y) evaluated from 0 to π/2.
Finally, we evaluate the outer integral to get the final answer.