Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13, Problem 10SP
To determine
To find: the
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1. Find the line integral in a vector field
F. dr, where F = (y, x + 2y) and C is
a curve consisting of 2 parts. First, the straight line from (-1,1) to (1,1), followed by
the parabola y = x² from (1,1) to (2,4). You must show all your work.
6.1.1
5. Show that F= (y cos(x),sin(x)+ y) is a conservative vector field and use this to
calculate the work done by F in moving a particle from (7/4,1) to (27/3,3).
Chapter 13 Solutions
Calculus
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- In the images below, the vector field F is shown by the blue arrows and the curve Cis shown in red. Indicate the value of F ·dT. 1. /, F ·dÌ = 0 2. ,F ·dT > 0 3. F dT < 0 4. The value of F ·dT cannot be determined with only this information. Xarrow_forward6. Compute fF dr where f(x, y) = (y² cos x, 2y sinx) and C is the straight line path starting at (1,1) and ending at (1,3). Hint: is the vector field conservative? (Answer: 8 sin 1)arrow_forward3. Let F = (x - y, xy) and C be arc of the circle x? + y? = 4 traversed counter-clockwise from (2,0) to (-2,0). A sketch of the vector field a curve are below. (a) Using the image above, determine whether F- dr is positive or negative. (b) Evaluate | F . dĩ. You may use that sin?(t) = /2. (Hint: the answer is 16/3 + 27)arrow_forward
- Not zero.arrow_forwardDetermine which theorem applies to simplify the following. It is possible that more than one will apply. = Find the work done by the vector field F(x, y) · yz cos(xy)i + xz cos(xy)j + sin(xy)k along the positively oriented triangle with vertices (2,1,-6), (3,-1,1), and (0,1,0). оооо Fundamental Theorem of Line Integrals Green's Theorem Stoke's Theorem The Divergence Theoremarrow_forwardA net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x - y, z + y +7,z²) and the net is decribed by the equation y = √1-x²-2², y 20, and oriented in the positive y-direction. (Use symbolic notation and fractions where needed.) 1.45-1 yasarrow_forward
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