Suppose that f(x) = 4 - x^2
a. Partition the interval [1,2] into 4 subintervals, identify the subintervals, and sketch the rectangles associated with the Right Riemann Sum.
b. Calculate the total area for the rectangles in part a.
c. Does the total area of the rectangles give an underestimate or overestimate of the definite integral ∫2 to 1 4 - x^2 dx? Try to give an answer based on the behavior of the curve y = 4 - x^2 instead of actually evaluating the given definite integral.
Please Help!

Question

Suppose that f(x) = 4 - x^2
a. Partition the interval [1,2] into 4 subintervals, identify the subintervals, and sketch the rectangles associated with the Right Riemann Sum.
b. Calculate the total area for the rectangles in part a.
c. Does the total area of the rectangles give an underestimate or overestimate of the definite integral ∫2 to 1 4 - x^2 dx? Try to give an answer based on the behavior of the curve y = 4 - x^2 instead of actually evaluating the given definite integral. 
Please Help!

turingtest · Answer

|dw:1340562834728:dw|looks like this is the interval they want

turingtest · Answer

each subinterval has size$$\Delta x={b-a\over n}$$where the interval is [a,b] and we are partitioning it into n segments

turingtest · Answer

what is $\Delta x$ in your case?

anonymous · Answer

Okay, so then that would be 2-1/4= 1/4?

turingtest · Answer

yes, so $$\Delta x=\frac14$$for you
now we need to make sure we get the right-hand endpoints...|dw:1340563102232:dw|hm... I hope that's right, using the right hand points makes the last rectangle area zero, but oh well...