Approximating the Area Between a Curve and the $x-$axis $-$ Part II

Again, consider the area between $f(x)=-x^2+3x-1$ and the $x-$axis on the interval $0,4.$

a$)$ Using technology, approximate the area using the given method and the number of rectangles. For example, you can do a google search for "wolframalpham Riemann sums calculator."

$\backslash$table$[[,n=10,n=100,n=1000$

a$)$ Show that $x=\frac{4}{n}.$

b$)$ Show that $x_k=\frac{4k}{n}.$

c$)$ Show that $f(x_k)=-\frac{16k^2}{n^2}+\frac{12k}{n}-1$

d$)$ Finally, $f(x_k)*x=-\frac{64k^2}{n^3}+\frac{48k}{n^2}-\frac{4}{n}$