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
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
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
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. Consider the area of the region that lies inside the curve given in polar form) by r = 6 sin(@) and outside the cardioid given by r=2+2 sin(0). (a) (3pts) Set up but do not evaluate an integral(s) which represents the area of this region. (b) (3.5pts) Evaluate this integral to determine the exact area of this region. (Hint: you will need to use a trig, identity)