Difference between revisions of "009B Sample Final 3, Problem 1"

Revision as of 10:46, 18 February 2017

Divide the interval $[-1,1]$ into four subintervals of equal length ${\frac {1}{2}}$ and compute the left-endpoint Riemann sum of $y=1-x^{2}.$

Solution:

(a)

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

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-<span class="exam">Consider the region bounded by the following two functions:
+<span class="exam">Divide the interval <math>[-1,1]</math> into four subintervals of equal length <math>\frac{1}{2}</math> and compute the left-endpoint Riemann sum of <math>y=1-x^2.</math>
-::::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math style="vertical-align: -4px">y=0</math>.
-<span class="exam">a) Using the lower sum with three rectangles having equal width, approximate the area.
-<span class="exam">b) Using the upper sum with three rectangles having equal width, approximate the area.
-<span class="exam">c) Find the actual area of the region.
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