<p>Can somebody explain to me the methodology for doing #17 and 18 from this test?</p>
<p>Frankly, I'm horrified that I cannot figure these out. Please help!</p>
<p>lol, i solved number 17 a few days. Afraid, I can’t solve 18 since I have no knowledge of Riemann Sum.</p>
<p>Total area of that loop is 2 because int[cos(x),x,-pi/2,pi/2]. </p>
<p>Area of the rectangle is A=2xy=2x cos x since y=cos x.</p>
<p>The area of the shaded curve is A=2-2x cos x</p>
<p>Solve for x using your graphing calculator.
The first answer whose x is within the interval -pi/2 and pi/2 is the answer.</p>
<p>And I got B because</p>
<p>A).799=2-2x cos x; Solve for x and x=-42.3973, -14.1795,-4.58092,-1.89351,4.83686. This answer is no good because none of its solution is within -pi/2 and pi/2.</p>
<p>B).878=2-2x cos x; Solve for x and x=-42.3983,-14.1767, -4.58986,-1.8747,.8506,.869955,4.82883. Hey look two solutions are within the domain of -pi/2 and pi/2. Therefore, B is the answer because of the reason and because it is the minimum area.</p>
<p>Wait, is it part 1 or part 2??</p>
<p>^Part 2, BC.</p>
<p>If you see a graph of a loop and a rectangle, that’s 17.</p>
<p>oh, sorry yes it was part 2 in the BC.</p>
<p>thanks for 17. however, now that you showed me that solution, I think i remember a better way: graph 2 - 2xcosx and find the minimum from -pi/2 to pi/2 using the graphing calc (you have to zoom in and choose bounds very close to the expected minimum), or find where the derivative changes sign from positive to negative when x is between -pi/2 to pi/2, instead of using guess and check.</p>
<p>anyone know how to do 18??</p>
<p>For 17 Yep i got the same thing, with the same work as jerrry
LOL 18 i have no idea too :(</p>
<p>How depressing.
Rn = i=1SIGMAn (deltaX)f(a+ideltaX), where deltaX = b-a/n
= i=1SIGMAn (2/n)f(a+2i/n)
= i=1SIGMAn (2/n)(1+3[2i/n])
= i=1SIGMAn (2/n)(1+6i/n)
So I got D. I could be wrong though, someone check.</p>
<p>D is right, thanks much!</p>
<p>Jerry, correct me if I’m wrong, but you differentiated 2xcosx incorrectly. It should be xcosx - 2xsinx. I still can’t get the answer though -_- I get 1.1221</p>
<p>derivative of 2xcosx = 2cosx - 2xsinx, not xcosx - 2xsinx. You should get the right answer after that.</p>
<p>
You differentiated it wrong. The first term should be 2cosx.</p>
<p>I think what MasterTTP was doing was finding where A_rectangle had a maximum by finding where A’ crossed the x-axis</p>
<p>MasterTTP, he wasn’t even differentiating 2x cos x</p>