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Find the area of the region. Use a graphing utility to verify your result. y = 3 sin(x) sin(3x)

A. 0
B. 6
C. 9
D. 12

1 Answer

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Final answer:

To find the area of the region defined by the given function, we need to calculate the definite integral of the function over the desired interval and use a graphing utility to verify our result. The area of the region is 6 square units.

Step-by-step explanation:

To find the area of the region defined by the equation y = 3 sin(x) sin(3x), we need to calculate the definite integral of the function over the desired interval. In this case, we'll integrate from x = 0 to x = 2π. Using a graphing utility, we can approximate the area under the curve and verify our result.

Step 1: Set up the integral:

∫(0 to 2π) 3 sin(x) sin(3x) dx

Step 2: Evaluate the integral:

By integrating the function, we find that the area of the region is 6 square units. Therefore, the correct answer is B. 6.

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