Riemann Sum

[KEYWEST17]

The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x)= -x^2/4 +2x on the interval (3,7)

The value of this left endpoint Riemann sum is ?

 

[galactus]

Just count up the area of the 8 rectangles. That is basically all it is.

Since you're starting at the left side of the rectangles, the height of the first rectangle is

$\displaystyle \frac{-(3)^{2}}{4}+2(3)=\frac{15}{4}$

The height of the second is $\displaystyle \frac{-(3.5)^{2}}{4}+2(3.5)=3.9375$

and so on. The last one will use x=6.5

The width of each rectangle is 1/2. Find the 8 heights, add them up, multiply the sum by 1/2.

There's your area.