(1 point) Evaluate the line integral ScF. dr, where F(x, y, z) = -4xi – 4yj + 5zk and C is given by the vector function r(t) = (sin t, cost, t), osts 31/2. 4
Evaluate & Fodr, where F(x, y, z) = (y² -2 2,5x) and C: 714) =<t", t, -tº), -15ts 1.
/// (1 point) Evaluate the triple integral 1 yd where D is the region in the first octant (z > 0, y 0,2 2 0 below the plane z = 1 y and with z
/// (1 point) Evaluate the triple integral 1 yd where D is the region in the first octant (z > 0, y 0,2 2 0 below the plane z = 1 y and with z
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
Evaluate
∫∫∫
E
√
x
2
+
y
2
+
z
2
d
V
where
E
lies above the cone
z
=
√
x
2
+
y
2
and between the spheres
x
2
+
y
2
+
z
2
= 1
and
x
2
+
y
2
+
z
2
= 9
.
df (76 KB) 2. Evaluate r2 + y2 + 22 dV x2 + y2 and between the spheres r? + y2 + 2 = 1 and...
(1) Evaluate in d z where is the rectangle with sides x = 1, x = -1, y =-, y = 31. ii- dz where C is any positively oriented closed curve around the origin.
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
:) IS (x+y+z)ds X-1 (b): Find the work done by F over the curve in the direction of increasing t, where F =< x² + y, y2 + 1, ze >, r(t) =< cost, sint,t/27 >, Osts 27. y-2=2-3 =+ C) -1-2 I-3
9. Evaluate the “vector valued” line integral 1.Podr Fodr where F(x, y, z) = (x, y, zy) TT and C is given by r(t) = (sint, cost, t), with N » 4. u sta
Evaluate the double integral [ f(z,y) dady, where f (z,y) = 22 +y R and R is the region bounded by the lines y = 1, y = 0, 1 = 1.