16.219 please dtas117091-3 1-21 -1کا کا کاgr5052010:31 1 ₁ ^-+-tad wods for11-EC₁on what ori ! STulsi sonol al0-2+1st18. The figure shows a vector field F and two curves C₁ and C₂.Are the line integrals of F over C₁ and C₂ positive, negative,or zero? Explain. 1019. F(x, y) = xy²i - x² j,.LYAĮf✓r(t) = t³i+t²j, 0≤t≤1pavelکه که211 1C₂117→→19-22 Evaluate the line integral e F dr, where C is given bythe vector function r(t).21. F(x, y, z) = sin xi + cos y j + xz k,r(t) = t³i- t²j + tk, 0≤ t ≤ 1X>→→→→20. F(x, y, z) = (x + y²)i + xz j + (y + z) k,r(t) = t²i+t³j2tk, 0≤t≤2X22. F(x, y, z) = xi+yj + xyk,r(t) = cos ti+ sin tj + tk, 0≤t≤ T23-26 Use a calculator to evaluate the line integral correct tofour decimal places.23. F. dr, where F(x, y) = √√x+yi+ (y/x) j andr(t) = sin²ti+ sint cos tj, π/6 ≤ t ≤ π/3he line inteor zero. Then evaluate the27. F(x, y) = (x - y)i +C is the arc of the circclockwise from (2, 0)28. F(x, y)X√√x² + y²C is the parabola y ==29. (a) Evaluate the lineF(x, y) = e¹ir(t) = t²i+t³jCAS(b) Illustrate part (a)puter to graph Ccorresponding to30. (a) Evaluate the lineF(x, y, z) = xir(t) = 2ti+ 3:(b) Illustrate part (athe vectors fromt = ±1 and ±CAS 31. Find the exact valuewith parametric equz=e¹, 0≤t≤232. (a) Find the workF(x, y) = x²iaround the circclockwise dire(b) Use a computeand circle on tyour answer to33. A thin wire is bentx² + y² = 4₁ x >find the mass and34. A thin wire has thcircle with centerfunction is p(x, y)of the wire.35. (a) Write the formof mass (x, ycurve C if the

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SUORUME 2010 on 01852 31 19-22 Evaluate the line integral je F. dr, where C is given by the vector function r(t). 19. F(x, y) = xy²i – x² j, r(t) = t³i+t²j, 0≤ t ≤1 20. F(x, y, z) = (x + y²)i + xzj + (y+z)k, r(t) = t² i + t³j - 2tk, 0≤ t ≤2 21. F(x, y, z) = sin xi + cos y j + xzk, r(t) = t³i- t² i + tk 0≤t≤1 CAS 32. (a) Find F(x, arou clock (b) Use and your 33. A thin w x² + y² find the