Question

Find the area of the region enclosed between y = 3sin(x) and y = 3cos(x) from x = 0 to x = 0.3π .

Answer 1

The area of the region enclosed between y = 3sin(x) and y = 3cos(x) from x = 0 to x = 0.3π is found by integrating the difference between the two functions over the given interval and calculating the value of the definite integral.

Step-by-step explanation:

The question pertains to finding the area of a region enclosed between two curves over a specified interval on the x-axis. To find the area between the curves y = 3sin(x) and y = 3cos(x) from x = 0 to x = 0.3π, one must integrate the difference between the two functions over the given interval.

Here's a step-by-step explanation:

1. Identify the upper curve and the lower curve within the interval. It may require evaluating the functions at specific points or using their known properties.
2. Set up the integral to calculate the area between two curves. In this case, the integral will be from x = 0 to x = 0.3π of the difference 3cos(x) - 3sin(x).
3. Perform the integration to find the total area enclosed between the curves.
4. Calculate the numerical value of the definite integral to find the area.