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Using the Fundamental Theorem for line
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Calculus: Early Transcendentals (3rd Edition)
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- 5. Prove that the equation has no solution in an ordered integral domain.arrow_forwardSHOW COMPLETE SOLUTION. PLEASE MAKE THE SOLUTION/HANDWRITING CLEAR. THANKYOU!arrow_forwardUse Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $(5) (5x+ sinh y)dy - (3y² + arctan x²) dx, where C is the boundary of the square with vertices (1, 3), (2, 3), (2, 4), and (1,4). false (Type an exact answer.) (5x + sinh yldy – (3y® + arctan x an x²) dx = dx = ...arrow_forward
- Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line integral, and then evaluate the line integral using this theorem. v(e -X sin y) • dr, where C is the line from (0,0) to (In 5,7) C Select the correct choice below and fill in the answer box to complete your choice as needed. O A. The Fundamental Theorem for line integrals can be used to evaluate the line integral because the function is conservative on its domain and has a potential function p(x,y) =| (Type an exact answer.) O B. The function is not conservative on its domain, and therefore, the Fundamental Theorem for line integrals cannot be used to evaluate the line integral. Click to select and enter vOur answer(s and then click Check Answerarrow_forwardGreen’s Theorem for line integrals Use either form of Green’sTheorem to evaluate the following line integral.arrow_forwardUse Green's theorem to evaluate the line integral for the curve C given In the figure. [2y dx + x dy] (2,5) -2 -1 (-1, -1) (1,-1) -2 nswerarrow_forward
- 15.3 7arrow_forwardEvaluate the line integral by the two following methods. (IMAGE)arrow_forwardEvaluate. The differential is exact. HINT: APPLY: Fundamental theorem of line integral. The initial point of the path is (0,0,0) and the final point of the path is (4,5,1) (4.5, 1) (2x1²-2xz2²) dx + 2x²y dy-2x²z dz 10.00 768 OO 384 416arrow_forward
- a) Evaluate y? dydx. b) Evaluate the line integral Cos x cos y dx + (1 – sin x sin y) dy - where C is the part of the curve y = sin x from x = 0 to x = T/2.arrow_forwardcal 3 helparrow_forwardEvaluate F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. IC S cos(x) sin(y) dx + sin(x) cos(y) dy 9 (371) 2 C: line segment from (0, -) to T 2arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,