Final answer:
To sketch the region of integration, we need to understand the limits and shape of the region described by the given integral expression. The first integral represents a region above one curve and below another, while the second integral represents a region above one curve and below another. The limits of integration determine the boundaries of these regions.
Step-by-step explanation:
To sketch the region of integration for the given expression, we need to understand the limits and the shape of the region. The first integral is ∫₁₀ ∫√(y-√y) dxdy and the second integral is ∫₁⁴ ∫√(y√y-2) dxdy.
For the first integral, the limits of x are from √(y-√y) to √(y). The limits of y are from 1 to 10. This represents the region above the curve y = √(y-√y) and below the curve y = √(y).
For the second integral, the limits of x are from √(y√y-2) to √(y). The limits of y are from 1 to 4. This represents the region above the curve y = √(y√y-2) and below the curve y = √(y).