Question 19 1 pts Compute the volume SSSx 1dV where X is the solid defined by...
Compute the volume SSSx 1 dV where X is the solid defined by x2 + y2 < 4,0 Sz<10., A) 20 B) 407 C) 201 D) 801 ОА ОС OD OB Question 20 What is the absolute value of the Jacobian of : x = uv, y = u2 + v2 at the input point (u, v) = (2, 3)?
a) Sketch the three-dimensional solid that sits above theparaboloid z = x2 + y2 and below thesurfacez = √( x^2 +y^2)<this second one is a down-pointing cone>b) compute the volume of the solid you justsketchedshow work for part bthanks
Question 4. (20 pts) Use polar coordinates to find the volume of the solid between z = x2 + y2 and z= = 3 – x2 - y2
Question 4. (20 pts) Use polar coordinates to find the volume of the solid between z = x2 + y2 and 2 = 3 - 22 - y2.
MAT MATH213 Lectur... X © 10/12 142% 10 Problem 4- Compute the volume of the solid inside the sphere x2 + y2 + x2 = Rº between the two planes z = a and 2 = b where 0 <a<b<R. 2 R² = a + (² R²= 6² + ď 61 R y С
1) a.(20 pts) Set up the integral corresponding to the volume of the solid bounded above by the sphere x2+y2 + z2 16 and below by the cone z2 -3x2 + 3y2 and x 2 0 and y 20. You may want to graph the region. b. (30 pts) Now find the mass of the solid in part a if the density of the solid is proportional to the distance that the z-coordinate is from the origin. Look at pg...
Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) (5 pts] Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts] By using Stokes' Theorem, evaluate the line integral F. dr C where F(x, y, z) = (y2 + cos x)i + (sin y +22)j + xk
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. (b) [20 pts] By using Stokes’ Theorem, evaluate the line integral| vi F. dr where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) [5 pts) Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts) By using Stokes' Theorem, evaluate the line integral F. dr с where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
Question 4 5 pts x2 (A) X Ev Evaluate S 0 - 23azdy + cos,+C X (B) -cos-x+C V1-x2 -cos-x+C -r? + cos2x+c (D) - OD B ОА Question 6 5 pts + Evaluate s da. 6V22 +6 A) 3/72 +6 - 3In XV6 (B) 31n x + 12 +6 + c TV +6 2 (C) 22 +6 - 31n|a + v82 +6|+0 (D) xV22 +6 -2.101x + 4x2 +6|+c 2. 12 ОА D B Oc Question 19 5 pts...