-
Stewart
Evaluate the line integral \(\int_C 2+x^2y\,\mathrm{d}s\)
where \(C\) is the upper half of the unit circle \(x^2+y^2=1.\)
-
Stewart
Evaluate \(\int_C y^2\,\mathrm{d}x + x\,\mathrm{d}y\)
along two different paths \(C:\)
first the line segment from \((-5,-3)\) to \((0,2),\)
then the arc of the parabola \(x=4-y^2\)
from \((-5,-3)\) to \((0,2).\)
-
Stewart
Evaluate \(\int_C y\sin(z)\,\mathrm{d}s\)
where \(C\) is the circular helix defined parametrically
by the equations \(x=\cos(t)\) and \(y=\sin(t)\) and \(z=t\)
for \(0\leq t \leq 2\pi.\)
-
Stewart
Evaluate the line integral
\(\int_C y\,\mathrm{d}x + z\,\mathrm{d}y + x\,\mathrm{d}z \)
where \(C\) consists of the line segment
\(C_1\) from \((2,0,0)\) to \((3,4,5),\)
followed by the vertical line segment
\(C_2\) from \((3,4,5)\) to \((3,4,0).\)
Review Before Next Class
-
Stewart §5.4
A variable force of \(4\sqrt{x}\) newtons
moves a particle along a straight path
when it is \(x\) meters from the origin.
Calculate the work done in moving the particle
from \(x=4\) to \(x=16.\)
-
Stewart §12.3
A wagon is pulled a distance of 100 m
along a horizontal path by a constant force of 70 N.
The handle of the wagon is held at an angle of 35°
above the horizontal.
Calculate the work done by the force.