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Using the Fundamental Theorem of Line
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Calculus (MindTap Course List)
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- What is the geometrical meaning of an integral of a vector function?arrow_forwardEvaluating line integrals Use the given potential function φ of the gradient field F and the curve C to evaluate the line integral ∫C F ⋅ dr in two ways.a. Use a parametric description of C and evaluate the integral directly.b. Use the Fundamental Theorem for line integrals. φ(x, y, z) = (x2 + y2 + z2)/2; C: r(t) = ⟨cos t, sin t, t/π⟩ , for 0 ≤ t ≤ 2πarrow_forward人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT Find the integral of the vector function F(t)=(f.,cost)arrow_forward
- Stokes' Theorem (1.50) Given F = x²yi – yj. Find (a) V x F (b) Ss F- da over a rectangle bounded by the lines x = 0, x = b, y = 0, and y = c. (c) fc ▼ x F. dr around the rectangle of part (b).arrow_forwardWork by a constant force Evaluate a line integral to show thatthe work done in moving an object from point A to point B in thepresence of a constant force F = ⟨a, b, c⟩ is F ⋅ AB.arrow_forwardDetermine the type of points on the X (u, v) = (u, v, u?) surface. Differential geometryarrow_forward
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