Evaluate the following integral for a > 1 Sº 64x3 (x4 + 1) de 4a(a4 +...
Question 3 Using (P)(1-P) P 0<P <1 Evaluate the following integral 4 dy • 1+ Solution
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(2) Use Stokes' Theorem to evaluate the integral F.dr, where F(x, y, z) =< -Y, I, z > and where S is the upper hemispherical surface defined by z = v1- 2 - y2. The boundary of S is the curve C defined by Cos (t) y= sin (t) 0t 27 Z=0
(1 point) Using polar coordinates, evaluate the integral ST sin(x2 + x>)dA where Ris the region 1 5x2 + y2 549. 1.080
17.3 Evaluate the following integral: SSR cosh(x + y)dA where R is the region bounded by x > 0, y = 0 and the line x + 2y = 2.
1. Let F(x,y,z) =< 32, 5x, – 2y >. Use Stokes's Theorem to evaluate the integral Scurl F.ds, where S is the part of the paraboloid z = x² + y2 that lies below the plane z = 4 with upward- pointing normal vector.
(1 point) If f(x) = { 6x, x39 8 x >9 Evaluate the integral 10 6.". f(x) dx |
Evaluate the double integral integral | | =+ wy? + rʻydA R where R= {(x,y) 1<x<2,1 <y<2} Double Integral Plot of integrand and Region R 300- 1] 1] 200 1] 100 0 -100 /1) /1) 0/1) 0/1) (0/1) 3/19 ersion -200 -300 101234 This plot is an example of the function over region R. The region and function identified in your problem slightly different Preview Answer Round your answer to four decimal places
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2. Evaluate the surface integral F. dS, where F(x, y, z) = xi+yj+zk is taken over the paraboloid z=1 – x2 - y2, z > 0. SA errom bove de SS (-P (- Puerto Q + R) dA dy
Problem 1 <15 points> Figure shows a volume that conforms to the spherical coordinate system. The volume current density on the top surface is given as J R cos 0+ in0 + pR .Calculate the total current / passing through the top surface (4,00,360°) 4,300,00) You can use an online integral calculator if you need to find the closed form solution of a complex integral. Here is one: http://www.wolframalpha.com/calculators/integral-calculator/ 0,00,00)
1. (15 pts) Evaluate the following integral: 171*** v2 + y2 +7 derdy de