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1) For the function f(x) = x2 + 3, find a formula for the upper sum obtained by dividing the interval [0, 3] into n equal subintervals. Then take the limit as n→∞ to calculate the area under the curve over [0, 3] 

 

2) For the function f(x) = 36 – x2 , find a formula for the Riemann sum obtained by dividing the interval [0,6] into n equal sub intervals and using the right-hand endpoint for each Ck. Then take a limit of these sums as n–>infinity to calculate area under the curve

 

3)Use finite approximations to estimate the area under the graph of the function f(x) = 25 – x^2

between x = -5 and x = 5 using

  1. (a)  a lower sum with two rectangles of equal width

  2. (b)  a lower sum with four rectangles of equal width,

  3. (c)  an upper sum with two rectangles of equal width,

  4. (d)  an upper sum with four rectangles of equal width. 

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