Write the integrand of this line integral df and then evaluate the integral. [Hint: To find dx and solve for the partials given the integrand.] af f(x, y, z) recall that df = 0 dx + dy + af дх (0,5,1) дх af дх [ sin y cos x dx + cos y sin x dy + 3 dz (1,0,0)
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- 5. Prove that the equation has no solution in an ordered integral domain.integral zVT: V125 – 23 dr in terms of Beta function. Express theShow that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) 5 5x¹y dx + (x³ -z¹) dy - 4yz³ dz (0,0,0) Compute the paruar derivative. ƏM = 0 əz Compute the partial derivative. ap = 0 ax Compute the partial derivative. ƏN = 5x+ ax Compute the partial derivative. ƏM = 5x ду Select the correct choice below and fill in any answer boxes within your choice. (1,2,3) 5x¹y dx + (x³ -z¹) dy - 4yz³ dz = [ A. (0,0,0) (Type an exact answer.) B. The differential form is not exact.
- Identify the u, du, the form of the integralCalculate the line integral f(3xy³ − 4x + 4y + 8) dx + (−3xy+5) dy, where C' is the rectangle with vertices (2, −4), (2, -3), (−3,−3), and (−3,-4) oriented clockwise. Enter an exact answer. Provide your answer below: f(3x³ 4x + 4y + 8) dx + (−3xy + 5) dy =Use the given transformation to evaluate the integral. x - /| 2 Y dA, where R is the parallelogram enclosed by the lines x - 4y = 0, x - 4y = 2, 6x - y = 4, and 6x - y = 5; u = x - 4y, v = 6x – y 6x – y
- N3Evaluate F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. SF I (4z + 2y) dx + (2x − 3z) dy + (4x - 3y) dz (a) C: line segment from (0, 0, 0) to (1, 1, 1) (b) C: line segment from (0, 0, 0) to (0, 0, 1) to (1, 1, 1) (c) C: line segment from (0, 0, 0) to (1, 0, 0) to (1, 1, 0) to (1, 1, 1)explain 4
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