Clearly construct a triple integral of the form dz dy dx to find the volume of the nose of a vehicle constructed from the paraboloid y=2(x +z) and the vertical plane y=6. But do not evaluate the integral.
8. Clearly construct a triple integral of the form dz dy dr to find the volume of the solid shown. The solid is constructed by taking the paraboloid :=x2 + y and have the top cut by the plane z=4y. But do not evaluate the integral. 1 10 8 ry
Evaluate the integral cosh(r)dx dy dz Jo o
Evaluate the integral cosh(r)dx dy dz Jo o
(1 point) Evaluate the integral by changing to cylindrical coordinates. 2 ,2 (a2 +y2)32 dz dy dz 2L,2
(1 point) Evaluate the integral by changing to cylindrical coordinates. 2 ,2 (a2 +y2)32 dz dy dz 2L,2
kz (a) (10 pts.) Evaluate the integral dz. Hint: consider the rectangle with vertices at R and R+π. Show that the integral along the vertical segments vanishes as R -> oo, while the integral along the top segment is a constant multiple of the integral along the bottom segment. (b) (2 pts.) Using part (a), find the Fourier transform of 1/cosh z.
kz (a) (10 pts.) Evaluate the integral dz. Hint: consider the rectangle with vertices at R and R+π....
please explain and do in matlab
Problem 6. Consider the definite integral fo, sin(VE) cos( dz. Use n-100 and n = 300 separately, to find the Riemann sum for this integral. Keep at least four decimal places for your answer
Problem 6. Consider the definite integral fo, sin(VE) cos( dz. Use n-100 and n = 300 separately, to find the Riemann sum for this integral. Keep at least four decimal places for your answer
1. (а) Using an appropriate contour in the upper half plane, find the integral z-1 dz. (z - i)(z+3i)2 If the contour was closed in the lower half plane, explain how your (b) residue calculation would change.
y2 + 4z2 = 16 Clearly construct a triple integral of the form dz dy dx to find the volume of the solid shown. The upper surface is defined by the cylinder y? +422 = 16. But do not evaluate the integral. 4 x
Evaluate the following indefinite integral:
e VT -dz C
f(x, y, z) dz dy da as an iterated integral in the 4. (6 points) Rewrite the integral order dx dy dz.