Evaluate
14. Evaluate \(\int_{C} y^{3} d x-x^{3} d y, C\) is the circle \(x^{2}+y^{2}=4\) with counterclockwise orientation.
Homework Answers
Evaluate C is the circle
Evaluate \(\int_{C} y^{3} d x-x^{3} d y, C\) is the circle \(x^{2}+y^{2}=4\) with counterclockwise orientation.
(a): Evaluate
5. (5 points) (a): Evaluate \(\int_{1}^{2} \int_{0}^{2}\left(y+2 x e^{y}\right) d x d y\).(b): Evaluate \(\int_{0}^{1} \int_{0}^{x^{2}} \int_{0}^{x+y}(2 x-y-z) d z d y d x\).
9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation. 9. (Green's Theorem) Use Green'...
9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation.
9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation.
Exact answer/fraction
Evaluate \(\int_{C} \mathrm{~F} \cdot d \mathbf{r}\) using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results.$$ \int_{C}[4(2 x+7 y) \mathbf{i}+14(2 x+7 y) \mathbf{j}] \cdot d \mathbf{r} $$C: smooth curve from \((-7,2)\) to \((3,2)\)Evaluate \(\int_{C} \mathrm{~F} \cdot d \mathbf{r}\) using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results.$$ \int_{C} \cos (x) \sin (y) d x+\sin (x) \cos (y) d y $$C: line segment from \((0,-\pi)\) to \(\left(\frac{3 \pi}{2},...
be = Use Green's Theorem to evaluate F. dr where F (3xy – esin x ,...
be = Use Green's Theorem to evaluate F. dr where F (3xy – esin x , 7x2 + Vy4 + 1) and C is the boundary of the region bounded by the circle x2 + y2 = 4 in the first quadrant with counterclockwise orientation.
4. Use Stokes' Theorem to evaluate F dr. F(x,y,z)-(3z,4x, 2y); C is the circle x2 +...
4. Use Stokes' Theorem to evaluate F dr. F(x,y,z)-(3z,4x, 2y); C is the circle x2 + y2 4 in the xy-plane with a counterclockwise orientation looking down the positive z-axis. az az F dr-JI, (curl F) n ds and VGy, 1) Hint: use ax' dy
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'...
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
Give parametric equations that describe a full circle of radius R, centered at the origin with...
Give parametric equations that describe a full circle of radius
R, centered at the origin with clockwise orientation, where the
parameter t varies over the interval [0,22]. Assume that the
circle starts at the point (R,0) along the x-axis.
Consider the following parametric equations, x=−t+7, y=−3t−3;
minus−5less than or equals≤tless than or equals≤5. Complete parts
(a) through (d) below.
Consider the following parametric equation.
a.Eliminate the parameter to obtain an equation in x and y.
b.Describe the curve and indicate...
The graph of f is shown. Evaluate each integral by interpreting it in terms of areas
The graph of f is shown. Evaluate each integral by interpreting it in terms of areas.(a) \(\int_{0}^{10} f(x) d x\)(b) \(\int_{0}^{25} f(x) d x\)(c) \(\int_{25}^{35} f(x) d x\)(d) \(\int_{0}^{45} f(x) d x\)
Evaluate. 5 Sx(x2 - 16) 3 dx 4 5 [x(x2 - 16) º dx=0 (Type an...
Evaluate.$$ \int_{4}^{5} x\left(x^{2}-16\right)^{3} d x $$
9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation.
9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation.
be = Use Green's Theorem to evaluate F. dr where F (3xy – esin x , 7x2 + Vy4 + 1) and C is the boundary of the region bounded by the circle x2 + y2 = 4 in the first quadrant with counterclockwise orientation.
4. Use Stokes' Theorem to evaluate F dr. F(x,y,z)-(3z,4x, 2y); C is the circle x2 + y2 4 in the xy-plane with a counterclockwise orientation looking down the positive z-axis. az az F dr-JI, (curl F) n ds and VGy, 1) Hint: use ax' dy
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
Give parametric equations that describe a full circle of radius
R, centered at the origin with clockwise orientation, where the
parameter t varies over the interval [0,22]. Assume that the
circle starts at the point (R,0) along the x-axis.
Consider the following parametric equations, x=−t+7, y=−3t−3;
minus−5less than or equals≤tless than or equals≤5. Complete parts
(a) through (d) below.
Consider the following parametric equation.
a.Eliminate the parameter to obtain an equation in x and y.
b.Describe the curve and indicate...
Evaluate.$$ \int_{4}^{5} x\left(x^{2}-16\right)^{3} d x $$
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