To calculate: The area of the region
Answer to Problem 13RE
The area of the region is
Explanation of Solution
Given information:
Calculation:
To find the area of the region which is enclosed by the cosine curve
The sketch of these graphs will help us to more easily spot a given problem.
Let’s sketch the graphs into Desmos. Further by entering the code, see in the red rectangle below, mark the required region with the color.
By observing the given picture, notice that our area is bounded above with the
The points of intersection i.e. the limits of integration get by equalizing:
Since there is no simple method for finding solutions to this equation, use the Wolfram Alpha. By entering the
Into program the required values is
Let’s find the area of the green region. Therefore
To solve this obtained integral more simple, note that area is symmetric with the respect to the
Hence,
So let’s proceed with the calculation by using the Power formula and Trigonometric formula:
The area of the region equals
Where used previously that
Chapter 7 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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