Calculate the line integral over the vector field F(x, y, z) = 2yz + 3xj− yk along the curve C traced out by the position vector √(t) = −4tī+2t² j— 5th, t = [0, 1].
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Q: Calculate the line integral over the vector field F(x, y, z) = 2yz + 3xj− yk along the curve C…
A: The line integral is: L=−32=−0.667Explanation:
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Correct answer 22/3
![Calculate the line integral over the vector field
F(x, y, z) = 2yz + 3xj− yk
along the curve C traced out by the position vector
√(t) = −4tī+2t² j— 5th,
t = [0, 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F017b5c7e-49c0-46c7-a22b-9336d465c7c9%2Fb3fd234c-bb56-42dc-bd0f-f36b0f81e8a5%2Fuiqgqck_processed.jpeg&w=3840&q=75)
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- Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 1. Please show all your work.Let u(t) = 21'i+ (-1)j-8k. Compute the derivative of the following function. (11 +7t) u(t) Select the corect choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function O B. The derivative is the vector-valued function Di+ i+ k. Click to select and enter your answer(s) and then click Check AnswerCalculate the line integral of the vector field F = -3 i+ 2j along the line from the point (4, 0) to the point (12, 0). The line integral = -8
- A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)= 3xi + 2xyj + y ln zk moves along a path C where x = t?, y =t + 2, andz = 1+t Suppose a vector function F(x, y) starting from x = 9 and ending up with x = 36, determine the work by the vector function.Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function given as A° = ye"x + xe¯y on the line joining the two points.
- Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The paraboloid z = 3x2 + y2 and the parabolic cylinder y = 2x2 r(t) = (1,322 + 9^) * Need Help? Read ItCalculate the derivative (r × r'), where r = (5t, t²,e¹). dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) d (rxr') = (2te',-5e¹,0) dt Incorrect