Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the shaded region.
The x y coordinate plane is given. There are two curves, two horizontal lines, and a shaded region on the graph.
The first curve, labeled x = y2 − 5, enters the window in the fourth quadrant, goes up and left becoming more steep, crosses the y-axis at approximately y = −2.2, changes direction at the point (−5, 0), goes up and right becoming less steep, crosses the y-axis at approximately y = 2.2, and exits the window in the first quadrant.
The second curve, labeled x = ey, enters the window almost vertically just right of the y-axis, goes up and right becoming less steep, crosses the first curve just right of the y-axis at approximately y = −2.3, crosses the x-axis at x = 1, and exits the window in the first quadrant.
The first horizontal line, labeled y = −1, begins at the point (−4, −1) on the first curve, goes right, and ends at the approximate point (0.4, −1) on the second curve.
The second horizontal line, labeled y = 1, begins at the point (−4, 1) on the first curve, goes right, and ends at the approximate point (2.7, 1) on the second curve.
The region is right of the first curve, left of the second curve, above the first horizontal line, and below the second horizontal line.