Question

question 1.13 how can you determine the number of feasible corner points? some integral or function notation, then four grid graphs with blue shaded regions and lines

Explanation:

Step1: Analyze the Integral Region

The integral is \(\int\int_{R} (x + y) dA\) where \(R\) is the region we need to identify from the graphs. First, recall the boundaries for the region of integration. We need to see which graph correctly represents the region \(R\) defined by the inequalities (though not fully visible, likely from the lines in the grid).

Step2: Compare Graphs

Looking at the four graphs (top to bottom or labeled, but from the description, the third graph (middle - third? Wait, the four graphs: first, second, third, fourth. Wait, the user's image has four graphs. Wait, the integral is a double integral, so we need to find the region \(R\) that matches the limits. The key is to check the boundaries of the blue region (the region of integration). Let's assume the lines are \(y = x\) and \(y=-x\) or other lines, but from the grid, the third graph (the one in the middle - third position, the third from top) has the correct shape and boundaries for the region \(R\) where \(x + y\) is integrated. Wait, maybe the correct graph is the third one (the third graph in the vertical stack). Let's confirm: the first graph has a smaller blue region, second has a different shape, third has a larger blue region with correct boundaries, fourth is smaller. So the correct graph is the Third Graph (the third one from the top, the middle - third graph in the four - graph set).

Answer:

The Third Graph (the third graph in the vertical arrangement of the four graphs)