Finding the Area Bounded by Two Graphs In Exercises 15-30, sketch the region bounded by the graphs of the functions and find the area of the region. See Examples 1, 2, 3, and 4.
To graph: The region bounded by the graphs of
Given Information:
The region bounded by the graphs of
Graph:
Consider the following equations that give the required region,
It is a quadratic function. The term
The x-intercept is
Compute its y-intercepts as follows:
The y-intercept is
Consider the second function
It is a quadratic function. The term
The x-intercept is
Compute its y-intercepts as follows:
The y-intercept is
Compute the intersection point of the graphs of
Substitute
So two graphs intersect at point
Compute the x-intercept point of the graph of
So, x-intercept of the graph of
Compute the x-intercept point of the graph of
So, x-intercept of the graph of
Intersection point is calculated by,
Sketch the graph of the region as follows:
Formula used:
Area of a region bounded by two graphs is calculated using the following formula,
If f and g are continuous on
Power for integrals is,
Calculate:
From the above, the required area consists of two regions, left region and right region
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