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)
- 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_forwardEvaluating a Surface Integral. Evaluate ∫∫ f(x, y, z)dS, where S f(x,y,z)=√(x2+y2+z2), S:x2+y2 =9, 0⩽x⩽3, 0⩽y⩽3, 0⩽z⩽9.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 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_forwardUse Green's Theorem to evaluate the integral of F · dr. over C (Check the orientation of the curve before applying the theorem.) F(x, y) = (y2 cos(x), x2 + 2y sin(x)) C is the triangle from (0, 0) to (1, 3) to (1, 0) to (0, 0)arrow_forward
- Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. ∮C6 y2dx+3 x2dy∮C6 y2dx+3 x2dy, where CC is the square with vertices (0,0)(0,0), (3,0)(3,0), (3,3)(3,3), and (0,3)(0,3) oriented counterclockwise.arrow_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_forward(a) Find the Jacobian of the transformation x = u, y = uv(b) Sketch the region G: 1 ≤ u ≤ 2, 1 ≤ uv ≤ 2 in the uv-plane(c) Using the above transformation, transform the integral (picture included of integral) into an integral over G, and evaluate both integrals.arrow_forward
- Scalar line integrals Evaluate the following line integral along the curve C.arrow_forwardUSE COORDINATE CHANGE TO SLOVES THE DOUBLE INTEGRAL SHOWN IN THE PICTURE.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_forward
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