Exact answer/fraction

Question

Question

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 $\left(\frac{3 \pi}{2}, \frac{\pi}{2}\right)$

math calculus

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Add a comment

Answer 2

Similar Homework Help Questions

Find for the given F and C

Find $\int_{C} \vec{F} \cdot d r$ for the given $\vec{F}$ and $C$.$\cdot \vec{F}=-y \vec{i}+x \vec{j}+7 \vec{k}$ and $C$ is the helix $x=\cos t, y=\sin t r \quad z=t$, for $0 \leq t \leq 2 \pi .$$$ \int_{C} \vec{F} \cdot d \vec{r}= $$Find $\int_{C} \overrightarrow{\mathrm{F}} \cdot d \overrightarrow{\mathrm{r}}$ for $\overrightarrow{\mathrm{F}}=e^{y} \overrightarrow{\mathrm{i}}+\ln \left(x^{2}+1\right) \overrightarrow{\mathrm{j}}+\overrightarrow{\mathrm{k}}$ and $C$, the circle of radius 4 centered at the origin in the $y z$-plane as shown below.$$ \int_{C} \vec{F} \cdot d \vec{r}= $$
value of z= 96 Task 3: Answer the following

value of z= 96Task 3: Answer the following:a. Evaluate: $\int_{\frac{\pi}{2}}^{\pi} \boldsymbol{Z} \cos ^{3}(x) \sin ^{2}(x) d x$b. The moment of inertia, $I$, of $a$ rod of mass ' $m^{\prime}$ and length $4 r$ is given by $I=\int_{0}^{4 r}\left(\frac{Z m x^{2}}{2 r}\right) d x$ where $^{\prime} x^{\prime}$ is the distance from an axis of rotation. Find $I $Task 4: Answer the following:Using the Trapezoidal rule, find the approximate the area bounded by the curve$y=\boldsymbol{Z} e^{\left(\frac{x}{2}\right)}$, the $\mathrm{x}$ -axis and coordinates \(x=0,...
Use the Divergence Theorem to evaluate

Use the Divergence Theorem to evaluate $\iint_{S} \mathbf{F} \cdot d \mathbf{S}$, where $\mathbf{F}(x, y, z)=z^{2} x \mathbf{i}+\left(\frac{y^{3}}{3}+\cos z\right) \mathbf{j}+\left(x^{2} z+y^{2}\right) \mathbf{k}$ and $S$ is the top half of the sphere $x^{2}+y^{2}+z^{2}=4$. (Hint: Note that $S$ is not a closed surface. First compute integrals over $S_{1}$ and $S_{2}$, where $S_{1}$ is the disk $x^{2}+y^{2} \leq 4$, oriented downward, and $S_{2}=S_{1} \cup S$.)

PLEASE ANSWER ALL FIVE PROBLEMS

Find $\mathrm{dy} / \mathrm{dt}$.12) $y=\cos ^{5}(\pi t-8)$A) $-5 \pi \cos ^{4}(\pi t-8) \sin (\pi t-8)$B) $-5 \cos ^{4}(\pi \mathrm{t}-8) \sin (\pi \mathrm{t}-8)$C) $5 \cos ^{4}(\pi t-8)$D) $-5 \pi \sin ^{4}(\pi t-8)$Use implicit differentiation to find dy/dx.13) $x y+x=2$A) $-\frac{1+y}{x}$B) $\frac{1+y}{x}$C) $\frac{1+x}{y}$D) $-\frac{1+x}{y}$Find the derivative of $y$ with respect to $x, t$, or $\theta$, as appropriate.14) $y=\ln 8 x^{2}$A) $\frac{2}{x}$B) $\frac{1}{2 x+8}$C) $\frac{2 x}{x^{2}+8}$D) $\frac{16}{x}$Find the derivative of $\mathrm{y}$ with respect to $\mathrm{x}, \mathrm{t}$, or $\theta$, as appropriate.15) $y=\left(x^{2}-2 x+6\right) e^{x}$A)...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin...

Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
An object moves though a vector field.

1. ( 8 points) An object moves though a vector field, $\overrightarrow{\mathbf{F}}(x, y)$, along a circular path, $\overrightarrow{\mathbf{r}}(t)$, starting at $P$ and ending at $Q$ as shown in the graph below.(a) At the point $R$ draw and label a tangent vector in the direction of $d \overrightarrow{\mathbf{r}}$.(b) At the point $R$ draw and label a vector in the direction of the vector filed, $\overrightarrow{\mathbf{F}}(R)$.(c) At the point $R$ is $\overrightarrow{\mathbf{F}} \cdot d \overrightarrow{\mathbf{r}}$ positive, negative, or zero? Circle the correct...

Evaluete the line integral using the Fundamental Theorem of Line Integrats

Evaluete the line integral using the Fundamental Theorem of Line Integrats. Use a computer atgebra system to verify your results.$$ \int_{c}(2 yi+2 xj)=d r $$Ci smooth curve from $(0,0)$ to $(2,7)$.
Use a parametrization to find the flux

Use a parametrization to find the flux$\iint_{S} \mathbf{F} \cdot \mathbf{n} \mathrm{d} \sigma$of the field $\mathbf{F}=\frac{9 x \mathbf{i}+9 y \mathbf{j}+9 z \mathbf{k}}{\sqrt{x^{2}+y^{2}+z^{2}}}$ across the portion of the sphere $x^{2}+y^{2}+z^{2}=25$ in the first octant in the direction away from the origin.The flux is _______
Question 1. Determine whether or not

Question 1. Determine whether or not $\mathrm{F}(x, y)=e^{x} \sin y \mathbf{i}+e^{x} \cos y_{\mathbf{j}}$ is a conservative field. If it is, find its potential function $f$.Question 2. Find the curl and the divergence of the vector field $\mathbf{F}=\sin y z \mathbf{i}+\sin z x \mathbf{j}+\sin x y \mathbf{k}$Question 3. Find the flux of the vector field $\mathbf{F}=z \mathbf{i}+y \mathbf{j}+x \mathbf{k}$ across the surface $r(u, v)=\langle u \cos v, u \sin v, v\rangle, 0 \leq u \leq 1,0 \leq v \leq \pi$ with...

Given Show that

Given$$ \vec{F}(x, y)=\left\langle\frac{2 x^{3}+2 x y^{2}-2 y}{x^{2}+y^{2}}, \frac{2 y^{3}+2 x^{2} y+2 x}{x^{2}+y^{2}}\right\rangle $$Show that $\int_{C} \vec{F} \cdot d \vec{r}=4 \pi$ for any positively oriented simple closed curve that encloses the origin.

Exact answer/fraction

Homework Answers

Add Answer to:
Exact answer/fraction

Post as a guest

Earn Coins

Find for the given F and C

value of z= 96 Task 3: Answer the following

Use the Divergence Theorem to evaluate

PLEASE ANSWER ALL FIVE PROBLEMS

Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin...

An object moves though a vector field.

Evaluete the line integral using the Fundamental Theorem of Line Integrats

Use a parametrization to find the flux

Question 1. Determine whether or not

Given Show that

Exact answer/fraction

Homework Answers

Add Answer to: Exact answer/fraction

Post as a guest

Earn Coins

Add Answer to:
Exact answer/fraction