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Remember our city that straddles the Newton River? The city is applying for National Parks and Recreation funds and needs to know the area of the land (shaded in the diagram) within the city limits.

Given the equations of the riverbanks, determine the area of the land.   

North Bank:
South Bank:    

The -axis is the line pointing east, and the -axis is the line pointing north.

Set up an integral to find the area of the Northern region first.
Note that this will be the area between a horizontal line (on top) and a curvy line (on the bottom).

The area of the Southern region will be easier to set up.

First quadrant, x axis labeled east, y axis labeled north, origin labeled city hall, decreasing concave down curve starting about 1 fourth up on y axis, ending at x axis, horizontal distance to end point, labeled 8 miles, region below curve shaded, horizontal line at top, vertical distance from x axis labeled, 10 miles, periodic curve starting 3 fourths up on y axis, with 3 visible turning points, region between horizontal line & periodic curve shaded, both curves labeled, riverbanks.