Question

Evaluate $\int_C \mathbf{F} \cdot d\mathbf{r}$ if $\mathbf{F}(x, y) = \langle 3y - e^{\sin x}, 7x + \sqrt{y^4 + 1} \rangle$ and $C$ is the circle $x^2 + y^2 = 9$ oriented counterclockwise. Hint: Once you have set up the correct double integral using Green's Theorem, do not evaluate it from the inside-out as you normally would. Instead, think about what the double integral represents in terms of the region.

Name: Evaluate 𝐅· d𝐫 if 𝐅(x, y) = ⟨ 3y - e^sin x, 7x + √(y^4 + 1)⟩ and C is the circle x^2 + y^2 = 9 oriented counterclockwise. Hint: Once you have set up the correct double integral using Green's Theorem, do not evaluate it from the inside-out as you normally would. Instead, think about what the double integral represents in terms of the region.
Uploaded: 2020-12-14T03:56:04-08:00
Duration: 1 min 21 s
Channel: Hossam Mohamed
Description: Evaluate 𝐅· d𝐫 if 𝐅(x, y) = ⟨ 3y - e^sin x, 7x + √(y^4 + 1)⟩ and C is the circle x^2 + y^2 = 9 oriented counterclockwise. Hint: Once you have set up the correct double integral using Green's Theorem, do not evaluate it from the inside-out as you normally would. Instead, think about what the double integral represents in terms of the region.

          Evaluate $\int_C \mathbf{F} \cdot d\mathbf{r}$ if $\mathbf{F}(x, y) = \langle 3y - e^{\sin x}, 7x + \sqrt{y^4 + 1} \rangle$ and $C$ is the circle $x^2 + y^2 = 9$ oriented counterclockwise. Hint: Once you have set up the correct double integral using Green's Theorem, do not evaluate it from the inside-out as you normally would. Instead, think about what the double integral represents in terms of the region.

Evaluate 𝐅· d𝐫 if 𝐅(x, y) = ⟨ 3y - e^sin x, 7x + √(y^4 + 1)⟩ and C is the circle x^2 + y^2 = 9 oriented counterclockwise. Hint: Once you have set up the correct double integral using Green's Theorem, do not evaluate it from the inside-out as you normally would. Instead, think about what the double integral represents in terms of the region.

Added by Joshua B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hossam Mohamed

12/14/2020

Step 1

Green's Theorem states that for a vector field F = P i + Q j, the line integral of F around a simple closed curve C is equal to the double integral over the region D enclosed by C of (Qx - Py) dA, where Qx and Py are the partial derivatives of Q and P with respect Show more…

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Evaluate ∮_C F⋅dr if F(x,y)=3y-e^sinx,7x+y^4+1 and C is the circle x^2+y^2=9 oriented counterclockwise. Hint: Once you have set up the correct double integral using Green's Theorem, do not evaluate it from the inside-out as you normally would. Instead, think about what the double integral represents in terms of the region.