g(x) = 8 sin x, [0, pi], 6 rectangles

To approximate the area under the curve of the function g(x) = 8 sin(x) on the interval [0, pi] using rectangles, you would divide the interval into smaller subintervals and then find the height of each rectangle by evaluating the function at a specific point within each subinterval. Here's how you can do it with 6 rectangles:

1. Divide the interval [0, pi] into 6 equal subintervals. Since you have 6 rectangles, each subinterval will have a width of (pi - 0) / 6 = pi/6.

2. Start with the left endpoint of the first subinterval, x = 0. Evaluate the function g(x) = 8 sin(x) at this point to find the height of the first rectangle. g(0) = 8 sin(0) = 0, so the height of the first rectangle is 0.

3. Move to the right to the next subinterval. Evaluate the function at the left endpoint of this subinterval, x = pi/6, to find the height of the second rectangle. g(pi/6) = 8 sin(pi/6) = 4, so the height of the second rectangle is 4.

4. Repeat this process for each subinterval, evaluating the function at the left endpoint of each subinterval to find the height of the rectangle.

5. Calculate the area of each rectangle by multiplying its width by its height. The width of each rectangle is pi/6, as calculated in step 1.

6. Sum up the areas of all the rectangles to approximate the total area under the curve. The sum of the areas of the rectangles is (pi/6) * (0 + 4 + ... + height of the sixth rectangle).

Note that using more rectangles will result in a better approximation of the area under the curve. As you increase the number of rectangles, the width of each rectangle decreases, making the approximation more accurate.

left, right, or what?