6. (Complex line integrals) (a) Compute the integral 2 dz where y is that part of unit circle which lies the upper half plane, oriented from 1 to -1. (b) Compute the integral where I is the line segment from -2i to 2i.
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- Calculate the line integral shown in the image: Curve C runs counterclockwise and is formed by the union of the following curves: the line segment at point (3,4) to point (0,2), the arc of the parabola y = 2-x² from (0.2) the point P where the parabola cuts the negative half-axis of the x and the line segment connecting P to the point (3,4).8. Find the points on the cardioid r = sin(2θ) where the tangent line is horizontal. Draw.Resolve about the line x= -1 and use disk method. bound by y=x4, x=0, and y=16. Mark axis of rotation, draw and lable appropriate differential element, dimensions, and features.
- express the length of the curve as an integral but do not evaluate it. r = (2 − cos θ )−1, 0 ≤ θ ≤ 2πCalculate the complex integrals: Where α ∈ R is constant, C is the unit circle centered at the origin parameterized as z(t)= eit,t ∈ [-π,π]Obtain the differential equation of the family of plane curves described. 1. All ellipses having its centers at the origin and traverse axis x.
- Revolve about the line x= -1, use disk method. (Bound by y=x4, x=0, and y=16. Mark axis of rotation, draw appropriate differential elements on a graph, and lable all the appropriate dimensions and features.)Find the surface area resulting from the rotation of the parts in the first and fourth quadrants of the polar curve r = 1 - cos(θ) around the line θ=π/2, formulate only the necessary integral without solving it. Please solve a question quickly I need this Answer at half time Quickly. PleaseFind a parametrization of the right branch (x > 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh t and sinh t. How can you parametrize the branch x < 0?
- 1) Calculate the complex integrals with Cauchy's integral formula For W=0 and W=2, calculate according to the picture where C is the unit circle centered at the origin parametrized as z(t)= eit,t ∈ [-π,π]Find a parametrization for the path that travels along the graph of y=sinx from (0,0) to (pi,0).1) Calculate the complex integrals: For W=0 and W=2, calculate according to the picture where C is the unit circle centered at the origin parametrized as z(t)= eit,t ∈ [-π,π]