Find a function f(n) which gives the rightsum approximation for the area under the given curve from x = 3 to x = 9 using n rectangles.
To find the right sum approximation for the area under a curve using n rectangles, you need to divide the interval from x = 3 to x = 9 into n equal subintervals. Each subinterval will have a width of (9 - 3)/n.
The right sum approximation considers the height of the curve at the right endpoint of each subinterval. So, for each subinterval i, you need to evaluate the function at the right endpoint, which is given by x = 3 + (i * width) = 3 + (i * (9 - 3)/n).
The area of each rectangle is then calculated by multiplying the width of the subinterval by the height of the function at the right endpoint. So, the area of the i-th rectangle is (width * f(3 + (i * width))).
To find the total area under the curve, you need to sum up the areas of all the rectangles. So, the right sum approximation can be calculated using the following function:
f(n) = (9 - 3) / n * (f(3 + (1 * (9 - 3) / n)) + f(3 + (2 * (9 - 3) / n)) + ... + f(3 + (n * (9 - 3) / n)))
Note: Since we don't know the specific function that represents the curve, we use f(x) to represent that general function. You would replace f(x) with the actual function you are working with.