To sketch the region enclosed by the given curves, which are y = sin(x), y = 3x, x = π/2, and x = b (where b is an unknown value), we can follow these steps:
Plot the graphs of y = sin(x) and y = 3x on the same coordinate system.
Identify the points of intersection between the two curves. These are the points where sin(x) = 3x.
Determine the x-values where sin(x) = 3x. This can be done numerically or graphically.
Sketch the region enclosed by the curves y = sin(x), y = 3x, x = π/2, and x = b, based on the information obtained in step 3.
Determine whether to integrate with respect to x or y. To make this decision, consider the orientation of the curves and the region enclosed. Based on the given curves, it is likely that integrating with respect to x would be more suitable in this case.
Draw a typical approximating rectangle within the enclosed region. The rectangle should have one side parallel to the x-axis (or y-axis, depending on the decision made in step 5) and have dimensions that represent the width and height of the region.
Note: The value of b is not provided, so the specific shape of the region and the size of the rectangle cannot be accurately determined without that information