
Formula

'sida mdinats for Tle area r--4 siho (No need t evaluate ) beT5 2 'sida mdinats...
. Evaluate the fulówing intógrals: tle ioibwai erdz c-boundary ofe square with sides; z ±2、y= ±2 circle |s| 1 b+ cos@ b.
7) Consider the vector function r(t) = (cos(fit), In(t – 2), → a. Evaluate lim r(t) t-2+ b. Find r'(t) C. Evaluate Sr(t) dt
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of the function f(x, y) = 3 sin(ry) + cos(y2) cos 5t and y(t) = 5 sin t - sin 5t for 0 < t < 2« and F is the (5) EvaluateF dr where F(x, y) with counterclockwise orientation (2y, xy2and C is the ellipse 4r2 9y2 36 _ F dr where F(r, y) = (x2 -...
6(6pts) Sketch the curve and find the area it encloses. (SETUP DO NOT EVALUATE) r=1-2 cos 76pts) Find the area of the region that lies outside the first curves and inside the second curve. (SETUP DO NOT EVALUATE) r = 2 and r = 4cos
vortex (o,1.t) 1 2 hinklo,o) Vortex ot (o,t)at (o,o んhat is tle velocity vector op point A 2
vortex (o,1.t) 1 2 hinklo,o) Vortex ot (o,t)at (o,o んhat is tle velocity vector op point A 2
Assume te t and ne drag vind tunme l datas obteietlar na at plat torm area retaularing ot plattorn dea and stand ard sel Jevel Cond fion etermine Span eticeny tle Intt Slope
Assume te t and ne drag vind tunme l datas obteietlar na at plat torm area retaularing ot plattorn dea and stand ard sel Jevel Cond fion etermine Span eticeny tle Intt Slope
Evaluate the following integral in cylindrical coordinates. z T 4 4 dz r dr de 00-4 -4 4 T 4 4 SSS dz r dr do = (Type an exact answer, using a as needed.) 00-4
Evaluate Sc (2+2)dy where C is described by parametric equations x(t) = cos(t), y= sin(t), z = 2,0 <t< Select one: O A. +2 O B. 1+2 O C.-1 OD. -1 ABC is a triangle in R where A =(1,4,5), B =(2,-1,0) and C =(4, 2, -3). Find the area of ABC. Select one: O A. (-30,7, -13) O B. -2 OC. V1118 O D. VILLE
x = t^2 - 2t + 4, y = t^3 - 6t^2
8. a) Set up the integral you would need to evaluate to find the length of the curve given in #3 if Osts 10. b) Set up the integral you would need to evaluate to find the arclength of the curve r = 4sin(30), traced out once. 3
4 Let x(t) =-5(2t + 10) + 25(t)-056(t-2) Evaluate and sketch y(t) given by .t y(t) = | x(r)dr 13S)