Set up an integral for the area of the shaded region. Evaluate the integral to find the
x = y^2 - 6y
(-5, 5)
The x y coordinate plane is given. There are two curves and a shaded region on the graph.
The first curve, labeled x = 4y - y^2, enters the window in the third quadrant, goes up and right becoming more steep, passes through the origin, changes direction at the point (4, 2), goes up and left becoming less steep, crosses the x-axis at x = 4, passes through the graphed point (-5, 5), and exits the window in the second quadrant.
The second curve, labeled x = y^2 - 6y, enters the window in the fourth quadrant, goes up and left becoming more steep, crosses the first curve as it passes through the origin, changes direction at the point (-9, 3), goes up and right becoming less steep, crosses the first curve as it passes through the graphed point (-5, 5), crosses the x-axis at x = 6, and exits the window in the first quadrant.
The region is right of the first curve and left of the second curve.
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