Riemann Sums & Derivatives & Area of Accumulation Functions

Let  $$F\left(x\right)=\int_0^xf\left(t\right)dt$$  , where the graph of  $$f\left(x\right)$$  above consists of lines and a quartercircle. Determine  $$F\left(5\right)$$ . 

Let  $$F\left(x\right)=\int_0^xf\left(t\right)dt$$  , where the graph of  $$f\left(x\right)$$  above consists of lines and a quartercircle. Determine  $$F\left(7\right)$$ . 

Let  $$F\left(x\right)=\int_0^xf\left(t\right)dt$$  , where the graph of  $$f\left(x\right)$$  above consists of lines and a quartercircle. Determine  $$F\left(8\right)$$ . 

Let  $$F\left(x\right)=\int_0^xf\left(t\right)dt$$  , where the graph of  $$f\left(x\right)$$  above consists of lines and a semi-circle. Determine  $$F\left(6\right)$$ . 

Using the areas of each region given
$$\int_a^df\left(x\right)=$$  

Evaluate

(a)  

Use a midpoint Riemann Sum to approximate the area between 0 to 3 with 3 subintervals.

Based on the table, use a trapezoidal sum of 4 sub-intervals to estimate the area under the curve.

(calculator allowed for arithmetic)

Find the right-hand Riemann Sum, with three sub-intervals indicated by the table.

Find the Left-hand Riemann Sum, with three sub-intervals indicated by the table.