Area Between a Curve and the Coordinate Axis

1. If a function is continuous on the closed interval , the area between the curve , the -axis, and the two vertical lines and is given by:
   
2. Similarly, if a function is continuous on the closed interval , the area between the curve , the -axis, and the horizontal lines and is given by:
   

Area Between Two Curves

1. If two functions and are continuous on the closed interval , the area between the curves , , and the vertical lines , is:
   
2. Similarly, if two functions and are continuous on the closed interval , the area between the curves , , and the horizontal lines , is: