A graphing calculator is recommended . Use a graphing calculator Riemann Sum (fo
ID: 2887793 • Letter: A
Question
A graphing calculator is recommended
. Use a graphing calculator Riemann Sum (found here) to find the following Riemann sums.
f(x) = ex from a = ?1 to b = 1
(a) Calculate the Riemann sum for the function for the following values of n: 10, 100, and 1000. Use left, right, and midpoint rectangles, making a table of the answers, rounded to three decimal places.
n Left Midpoint Right (fill in the x's on the chart)
10 x x x
100 x x x
1000 x x x
(b) Find the exact value of the area under the curve by evaluating an appropriate definite integral using the Fundamental Theorem. The values of the Riemann sums from part (a) should approach this number. (Round your answer to three decimal places.) X square units
Explanation / Answer
n = 10 :
Left : 2.123
Right : 2.593
midpoint : 2.346
n = 100 :
Left : 2.327
Right : 2.374
Mid : 2.350
n = 1000 :
Left : 2.348
Right : 2.353
Mid : 2.350
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Integrating e^x, we get e^x
(e^x) from -1 to 1
e^1 - e^(-1)
e - 1/e
which is approx
2.350 ----> ANS