Physics equations/07-Work and Energy/Q:lineIntegral

Solutions (pdf)     Equations for this chapter        /Testbank/

Only version A of this testbank has been tested.

pe07lineIntegral-A
{Integrate the line integral of, $$\vec F = 9xy\hat x + 9.5y^3\hat y $$, along the y axis from  y = 5 to y = 14} +a) 8.98E+04  -b) 1.13E+05 -c) 1.42E+05  -d) 1.79E+05 -e) 2.25E+05  {Integrate the function, $$\vec F = r^7\theta^9\hat r + r^7\theta^5\hat \theta$$, along the first quadrant of a circle of radius 8} -a) 1.95E+07 -b) 2.36E+07  -c) 2.86E+07 -d) 3.47E+07  +e) 4.20E+07 {Integrate the line integral of $$\vec F = 4xy\hat x + 7.7x\hat y $$  from the origin to the point at x = 2.5 and y = 3.3} -a) 2.97E+01  -b) 3.74E+01 -c) 4.71E+01  +d) 5.93E+01 -e) 7.46E+01  {Integrate the function, $$\vec F = -x^2y^2\hat x + x^2y^3\hat y$$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1)}. Orient the path so its direction is out of the paper by the right hand rule} +a) 5.83E-01 -b) 7.07E-01  -c) 8.56E-01 -d) 1.04E+00  -e) 1.26E+00

pe07lineIntegral B
{Integrate the line integral of, $$\vec F = 7.8xy\hat x + 9.6y^3\hat y $$, along the y axis from  y = 6 to y = 16} -a) 9.73E+04  -b) 1.22E+05 +c) 1.54E+05  -d) 1.94E+05 -e) 2.44E+05  {Integrate the function, $$\vec F = r^8\theta^9\hat r + r^9\theta^3\hat \theta$$, along the first quadrant of a circle of radius 9} -a) 2.46E+09 -b) 2.98E+09  -c) 3.62E+09 -d) 4.38E+09  +e) 5.31E+09 {Integrate the line integral of $$\vec F = 2.9xy\hat x + 9.9x\hat y $$  from the origin to the point at x = 2.5 and y = 3.5} -a) 3.23E+01  -b) 4.07E+01 -c) 5.12E+01  +d) 6.45E+01 -e) 8.11E+01  {Integrate the function, $$\vec F = -x^5y^2\hat x + x^3y^5\hat y$$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1)}. Orient the path so its direction is out of the paper by the right hand rule} -a) 2.27E-01 -b) 2.75E-01  +c) 3.33E-01 -d) 4.04E-01  -e) 4.89E-01

pe07lineIntegral C
{Integrate the line integral of, $$\vec F = 6.3xy\hat x + 8.3y^3\hat y $$, along the y axis from  y = 3 to y = 16} -a) 1.08E+05  +b) 1.36E+05 -c) 1.71E+05  -d) 2.15E+05 -e) 2.71E+05  {Integrate the function, $$\vec F = r^7\theta^8\hat r + r^9\theta^9\hat \theta$$, along the first quadrant of a circle of radius 8} -a) 6.69E+09 -b) 8.11E+09  +c) 9.82E+09 -d) 1.19E+10  -e) 1.44E+10 {Integrate the line integral of $$\vec F = 2.9xy\hat x + 9.6x\hat y $$  from the origin to the point at x = 2.6 and y = 3.1} -a) 2.95E+01  -b) 3.72E+01 -c) 4.68E+01  +d) 5.89E+01 -e) 7.42E+01  {Integrate the function, $$\vec F = -x^2y^5\hat x + x^3y^5\hat y$$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1)}. Orient the path so its direction is out of the paper by the right hand rule} +a) 5.00E-01 -b) 6.06E-01  -c) 7.34E-01 -d) 8.89E-01  -e) 1.08E+00