(Last Updated On: December 8, 2017)
Let the Limit of n approaches to infinity (n → ∞)
Area Under a Curve
Formula: 

Example 1:  Find the area between y = 7 – x2 and the xaxis between the values x = –1 and x = 2.

Example 2:  Find the net area between y = sin x and the xaxis between the values x = 0 and x = 2π.

Area Between a Curve
The area between curves is given by the formulas below.
Formula 1:  
for a region bounded above and below by y = f(x) and y = g(x), and on the left and right by x = a and x = b.  
Formula 2:  
for a region bounded left and right by x = f(y) and x = g(y), and above and below by y = c and y = d.


Example 1:1  Find the area between y = x and y = x2 from x = 0 to x = 1. 


Example 2:1  Find the area between x = y + 3 and x = y2 from y = –1 to y = 1. 
credit: Bruce Simmons, Paul Dawkins (Lamar University)©2013 www.PinoyBIX.com
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