Chapter 5.1, Problem 21E

(a)

To determine

To sketch: The graph of $f\left(x\right)=\cos x$ on the interval $\left[0,\frac{\pi }{2}\right]$.

(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 $f\left(x\right)=\cos x$ on the interval $\left[0,\frac{\pi }{2}\right]$ for $n=4$; determine which Riemann sum underestimates and overestimates the area under the curve.

(d)

To determine

To find: The left and right Riemann sums of $f\left(x\right)=\cos x$ on the interval $\left[0,\frac{\pi }{2}\right]$.