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Calc 3 13.2

 

<== Calculus 3
Number Question Answer
See the work
1. Evaluate the line integral \displaystyle \int_C  x^5 z \; ds, where C is the line segment from (0,4,7) to (2,8,6).

150.134 The work
2. Evaluate the line integral \displaystyle \int_C 5 x y^4 \; ds, where C is the right half of the circle x^2 + y^2 = 25.

31250 The work
3. Compute the total mass of a wire bent in a quarter circle with parametric equations:
x = 5cos(t), y = 5sin(t), 0 &le t &le &pi/2 and density function 
ho(x, y) = x^2 + y^2.

196.35 The work
4. Let C be the curve which is the union of two line segments, the first going from (0, 0) to (-1, -4) and the second going from (-1, -4) to (-2, 0).
Compute the line integral \displaystyle \int_C -1 {dy}  + 4 {dx}.

-8 The work
5. Let F be the radial force field F = xi + yj. Find the work done by this force along the following two curves, both which go from (0, 0) to (4, 16).

A. If C_1 is the parabola: x = t, \ y = t^2, \ 0 \leq t \leq 4, then \displaystyle \int_{C_1} \mathbf{F} \cdot \, d\mathbf{r} =

B. If C_2 is the straight line segment: x = 4 t^2, \ y = 16 t^2, \ 0
\leq t \leq 1,
then \displaystyle \int_{C_2} \mathbf F \cdot \, d\mathbf{r} =

A) 136
B) 136
The work
6. Evaluate the line integral \int_C \mathbf{F}\cdot d\mathbf{r}, where F(x, y, z) = 4xi - 5yj - zk and C is given by the vector function
r(t) = &lang sin(t), cos(t), t &rang, 0 &le t &le 3&pi/2.

-6.6033 The work
7. Evaluate the line integral \int_C \mathbf{F}\cdot d\mathbf{r}, where F(x, y, z) = (5sinx)i - (4cosy)j + xzk and C is given by the vector function \mathbf{r}(t) = t^3 \mathbf{i} - t^2 \mathbf{j} + t^1 \mathbf{k} , 0 &le t &le 1.

5.864 The work
8. Find the work done by the force field F(x, y, z) = 1xi + 1yj + 7k on a particle that moves along the helix \mathbf{r}(t) = 2 \cos(t)\mathbf i + 2 \sin(t)\mathbf j + 5t\mathbf k, 0 \leq t
\leq 2\pi. 219.91 The work
9. question Answer The work
10. question Answer The work