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Using the Fundamental Theorem for line
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- 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 -* sin y) • dr, where C is the line from (0,0) to (In 3,1t) Select the correct choice below and fill in the answer box to complete your choice as needed. 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.arrow_forwardEvaluate fot F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. JC 1 [8(4x + 5y)i + 10(4x + 5y)j] · dr C: smooth curve from (-5, 4) to (3, 2) X Need Help? Read It Watch It Master Itarrow_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
- Using the Fundamental Theorem of Line Integrals, evaluate F. dr, where f(x, y, z) = cos(xx) + sin(xy) - xyz is a potential function for F, and C is any (1, 2). path that starts at and ends at (2, 5, -5).arrow_forwardUsing the Fundamental Theorem of Line Integrals, evaluate F. dr, where f(x, y, z) = cos(x) + sin(ay) – xyz is a potential (1, 2) function for F, and C is any path that starts at and ends at (2, 3, -2).arrow_forwardDetermine if Green's theorem can be used to evaluate the line integral. Then evaluate based on your finding. |(ex – 2y)dx + Iny dy, C: x=2cost, y= 3 + 2sint, Ost<2m Upload Choose a Filearrow_forward
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