Concept explainers
Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value of
To calculate: The value of the integral function
Answer to Problem 49E
The value of the integral function
Explanation of Solution
Given information:
The integral function is
The region lies between
Calculation:
The integral property 2 is shown below:
The property is valid only, if the functions
Apply the integral property 2 in Equation (1).
Rearrange Equation (3) as shown below.
Consider the regions A, B, and C bounded by the graph of f as in Figure 1.
Refer to Figure 1.
The value of the region which lies in the integral
The value of the region which lies in the integral
The value of the region which lies in the integral
Calculate the integral
Calculate
Consider the function
The function
Plot the function
Refer to Figure 2.
Take the area bounded by the function
Modify Equation (5) using the Figure 2.
Calculate
Calculate the integral function using Equation (4).
Substitute
Therefore, the value of the integral function is 15.
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