1 Evaluate the triple integral SS Sw 2x dV, where w is the sulid in 3-dimensional...
Evaluate the triple integral. ∭E5xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by the curves y = √x, y = 0, and x = 1
Problem 8
a. y" + 4y - sin (2 t) + + -1 b. 4y" - 4y + y = 164/2 8. Evaluate the triple integral SSS w 2x DV, where W is the solid in three-dimensional region bounded by the Surfaces 2 = x+y?, 2:21+y), 21
Evaluate the triple integral.
3z
dV, where E is bounded by the cylinder
y2 + z2 = 9 and the planes
x = 0, y = 3x, and z = 0 in the
first octant
E
(1 point) Use spherical coordinates to evaluate the triple integral dV, e-(x+y+z) E Vx2 + y2 + z2 where E is the region bounded by the spheres x² + y2 + z2 = 4 and x² + y2 + z2 16. Answer =
Evaluate the triple integral. SSS E 8x dV, where E is bounded by the paraboloid x = 5y^2 + 5z^2 and the plane x = 5.
My professor said " Hint: Use
change of variables formula u= xy, v= x^2 - y^2"
31. Consider the triple integral II w 2x dv, where W is the solid three-dimensional region bounded by the surfaces z = x2 + y2, z = 2(x2 + y2), and z = 1. Express it as an iterated integral in cylindrical coordinates. Do not evaluate it.
6. Express the triple SSSE f(, y, z) dv erated integral in three different ways dzdxdy, dxdydz and dydzdx, where E is the solid bounded by the given surfaces (Don't evaluate the integral) x = 2, y = 2, z = 0, x + y – 2z = 2
(1 point) Write limits of integration for the integral Sw f(x, y, z) dV, where W is the quarter cylinder shown, if the length of the cylinder is 3 and its radius is 2. Z Sw f(x,y,z) dV = SSS f(z,y,z)d d d where a = b= I d= and f (Note: values for all answer blanks must be supplied for this problem to be able to check the answers provided.)
Evaluate the triple integral. ∫∫∫E(x - y) dV, where E is enclosed by the surfaces z = x2 - 1, z = 1 - x2, y = 0, and y = 2
Use cylindrical coordinates to evaluate the triple integral J Vi +y2 dV, where E is the solid bounded by the circular paraboloid z 16 -1(z2 +y2) and the xy-plane.