Final answer:
The LRAM and RRAM of the function f(x) = sin^(-1)(x / 3) on the interval [0,3] with n = 6 is 1/2.
Step-by-step explanation:
To find the left Riemann sum (LRAM) and the right Riemann sum (RRAM) of the function f(x) = sin^(-1)(x / 3) on the interval [0,3] with n = 6.
We need to divide the interval into subintervals of equal width and evaluate the function at specific points within each subinterval.
For the LRAM, we evaluate the function at the left endpoint of each subinterval.
In this case, since we have n = 6 subintervals, the width of each subinterval is 3 / 6 = 1/2.
So, we evaluate f(x) at x = 0, 1/2, 1, 3/2, 2, and 5/2.
We sum up the values of f(x) at these points and multiply by the width of each subinterval, which is 1/2.
For the RRAM, we evaluate the function at the right endpoint of each subinterval.
So, we evaluate f(x) at x = 1/2, 1, 3/2, 2, 5/2, and 3.
We sum up the values of f(x) at these points and multiply by the width of each subinterval, which is 1/2.
Therefore the LRAM and RRAM of the function f(x) = sin^(-1)(x / 3) is 1/2.