Consider the integral given by $$\int_{0}^{\,4} {(x^2-3x)}\, dx$$

(a) Find an approximation to this integral by using a Riemann sum with right endpoints and n = 8. Your answer should be correct to four decimal places.

$R_8 =$

Using the following definition of the integral $$\int_a^b f(x)dx=\lim_{n\rightarrow\infty}\sum_{i=1}^n f(x_i)\Delta x$$ where $x_i$ are right hand endpoints.

(b) Determine $\Delta x$ and $x_i.$

$\Delta x =$

$x_i =$

(c) Using the definition mentioned above, evaluate the integral.

Value of integral: