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Workshop week 1

Workshop week 1 - Anthony Reverri Section 27 Workshop Week...

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Anthony Reverri Section 27 Workshop Week 1 This week’s workshop asks us to sketch the region R defined by 1 ≤ x ≤ 2 and 0 ≤ y ≤ 1/ x 3 . Essentially we are asked to sketch the shaded area defined by the integral. Shown below is this sketch. Next we are asked to find the number at point a which divides the area above in half. To find a, first we need to find the total area under the curve. This is done by solving the integral above. The work is shown below: = = - = - (- = Now that we know the total area is , we know that half the area is and all we have to do is find the point a that is defined on 1 ≤ x ≤ 2. To do this we need to set a as one of the boundaries on the integral and set the new integral equal to Doing this will allow us to solve for a point a which splits the area in half. The work for the process described above is shown below. -

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We get a to equal , however, we only want the positive answer because it satisfies the condition that a is defined on 1 ≤ x ≤ 2. The reason we get a negative answer is because the graph also
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