Finding u and du/dx In Exercises 1-8, identify u and
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Chapter 5 Solutions
Calculus: An Applied Approach (MindTap Course List)
- Check Stokes' Theorem, evaluating the two integrals of the statement, to F(x, y, z) = (y, −x, 0), the paraboloid S : z = x2 + y2, with 0 ≤ z ≤ 1, and n pointing out of S. Answer is 1/2arrow_forwardDouble integral to line integral Use the flux form of Green’sTheorem to evaluate ∫∫R (2xy + 4y3) dA, where R is the trianglewith vertices (0, 0), (1, 0), and (0, 1).arrow_forwardTriple integrals Use a change of variables to evaluate the following integral. ∫∫∫D yz dV; D is bounded by the planes x + 2y = 1, x + 2y = 2,x - z = 0, x - z = 2, 2y - z = 0, and 2y - z = 3.arrow_forward
- Using Cauchy's Theorem calculate the following integral and the singular points of the function, where C: z(t) = 3*cost(t) + i*(3+ 3*sin(t)) 0 < t < 2πarrow_forwardUsing polar coordinates, evaluate the integral (sin(x2+y2)dA) over the region 1<=x2+y2<=81.arrow_forwardSetup an integral to find the surface area for the graph y = x1/2 rotated about the y axis under the restriction that 1 < x < 4.arrow_forward
- calc 3 Evaluate the integral below, where E lies between the spheres x2 + y2 + z2 = 16 and x2 + y2 + z2 = 25 in the first octant.arrow_forwardRegion B: Computing the integral of the function f (x, y) = (x + y) cos (x + y), with a triangle consisting of vertices (0,0), (a, a) and (a, -a).arrow_forwardUSE COORDINATE CHANGE TO SLOVES THE DOUBLE INTEGRAL SHOWN IN THE PICTURE.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning