## Monday, March 11, 2013

### Area Bounded - Two Curves

Category: Integral Calculus, Analytic Geometry, Algebra

"Published in Newark, California, USA"

Find the area bounded by the given curves

Solution

To illustrate the problem, it is better to draw or sketch the graph of two given equations above by using the principles of Analytic Geometry as follows

 Photo by Math Principles in Everyday Life

Since the limits or their points of intersection are not given, then we have to solve their points of intersection using the two equations, two unknowns as follows

Subtract the second equation from the first equation, we have

Substitute the value of y to either of the two given equations in order to get the value of x as follows

Equate each factor to zero and solve for the value of x. The values of x are 3 and -1.

Their points of intersection are (-1, -4) and (3, -4).

Rewrite the two given equations as y = f(x), label further the figure, and use the vertical strip as follows

 Photo by Math Principles in Everyday Life

The area bounded by the two curves is given by the formula

Substitute the values of the limits and the two functions to the above equation, we have