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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
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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
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| 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
