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Evaluating a Line Integral In Exercises 23-32, evaluate
along each path. (Hint: If F is conservative, the
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Calculus: Early Transcendental Functions
- Linear Algebra question is attached.arrow_forward段階的に解決し、 人工知能を使用せず、 優れた仕事を行います ご支援ありがとうございました SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE AI | DON'T USE AI DON'T USE AI DON'T USE AI | 2. Evaluate the line integral function (x2-y2) dx, $(x2 - y2) dyy d(x2-y2) ds where cis given by x = 6 cost, y = 6 sintin an interval of 0 ≤ t≤2.arrow_forwardf(t) satisfies the integral equation: f(t) = 4e-3t H(t)-7/f(t-u) e-6u H(u) du Find the solution of the integral equation using Fourier transforms. Your answer should be expressed as a function of t using the correct syntax. f(t) =arrow_forward
- Let f: C → C be the function ƒ(z) = w z where w = u + iv is a fixed complex number. (a) Write down the formula for f viewed as a function ƒ : R² → R², i.e. give formulas for Re(f) and Im(f) in terms of x = Re(z) and y = Im(z). (b) Compute the total derivative Df₂ of ƒ at z as a 2 by 2 matrix with real entries. (c) Describe the linear transformation of the plane determined by this matrix and relate it to the complex number w.arrow_forwardPRACTICE EXERCISE A. Using the basic formulas, integrate the following: 1. S(x* – 2x3 + 3x² – 1)dx 2. S(2x – 5)²dx 3. S(2x + 3x? – 2)²dx 4. SE+dx 5.arrow_forwardThe complex function f(z)=u(x,y)+iv(x,y) can be differentiated at any point in the complex space. The real part of this function is given as u(x,y)=e−x[xsin(y)−ycos(y)].Determine the derivative of the function f(z) at z=i.arrow_forward
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