Chapter 5.1, Problem 22E

(a)

To determine

To sketch: The graph of $f\left(x\right)={\sin }^{-1}\left(\frac{x}{3}\right)$ on the interval $\left[0,3\right]$.

(b)

To determine

To calculate: The value of $\Delta x$ and the grid points.

(c)

To determine

To illustrate: The left Riemann sum and the right Riemann sum of the function

$f\left(x\right)={\sin }^{-1}\left(\frac{x}{3}\right)$ on the interval $\left[0,3\right]$ for $n=6$; determine which Riemann sum underestimates and overestimates the area under the curve.

(d)

To determine

To find: The left and right Riemann sums of $f\left(x\right)={\sin }^{-1}\left(\frac{x}{3}\right)$ on the interval $\left[0,3\right]$.