the exercises will be on file please

9. [-/0.12 Points] DETAILS SCALCET8 10.2.031. 0/100 Submissions Used MY NOTES ASK YOUR TEACH Use the parametric equations of an ellipse, x = a cos(0), y = b sin(0), 0 s 0 s 2n, to find the area that it encloses. Need Help? Read it Watch It 10. [-/0.12 Points] DETAILS SCALCET8 10.2.032.MI. 0/100 Submissions Used MY NOTES ASK YOUR TEACH Find the area enclosed by the curve x = t2 - 2t, y = vt and the y-axis. Need Help? Read it Master It 11. [-/0.12 Points] DETAILS SCALCET8 10.2.AE.005. 0/100 Submissions Used MY NOTES ASK YOUR TEACH y EXAMPLE 5 Find the length of one arch of the cycloid x = r(0 - sin(8)), y = (1 - cos(0)) SOLUTION From this example we see that one arch is described by the parameter interval 0 S 0 S 27. Since dx de and 2 ur x we have Video Example .() 10 V7 (1 - 2 cos( ) + cos ' (8 ) + sin ? ( 8 ) ) de = / V2(1 - cos (8 ) ) do. To evaluate this integral we use the identity sin?(x) = = (1 - cos(2x)) with 0 = 2x, which gives 1 - cos(0) = 2 sin2 . Since 0 SO S 217, we have O s S n and so sin(0/2) 2 0. Therefore V2(1 - cos(0)) = \\ 4 sin2(0/2) = 2 and so L = 2r sin(8/2) de = 2r = 27