Evaluate the following line integral.
Evaluate the following line integral. yzdx+xzdy +aydz, where c consists of straight-line segments joining (1,0,0) to (0,1,0) to (0,0,1) yzdx+xzdy +aydz, where c consists of straight-line segment...
7- Evaluate each of the following line integrals: (a) /xdy-ydx, c(t)-(cost,sint), 0<t<2π (b) xdx+ydy, c(t)-(cos(), sin,OSIS2 (c) yzdx +xzdy +xydz, where c consists of straight-line segments joining (1,0,0) to (0,1,0) to(0,0,1)
7- Evaluate each of the following line integrals: (a) /xdy-ydx, c(t)-(cost,sint), 0
Evaluate the triple integral SSST x2dv, where T is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,1,0), and (0,0,1)
1. Evaluate the complex integral: ∫C [zRe(z) − z¯Im(z)]dz, where C is the line segment joining −1 to i. (z¯ = z bar) 2. Evaluate the complex integral: ∫ C [iz^2 − z − 3i]dz, where C is the quarter circle with centre the origin which joins −1 to i.
(1 point) If C is the line segment from (7,4) to, (0,0), find the value of the line integral: Sc(3y2 7 + 2x1).dñ = ī (1 point) Find Sc((x2 + 3y)i + 5y37) . • dr where C consists of the three line segments from (1,0,0) to (1,1,0) to (0,1,0) to (0,1, 3). Sc((x2 + 3y)ī + 5y37). . dr =
8. (10 points) Use Stokes' Theorem to evaluate where (..) - (awy, 3) and C is the triangle with vertices (1,0,0), (0,1,0), and (0,0,1). You may orient either clockwise or counterclockwise (when looking down the positive z-axis), but you must indicate which orientation you used
2. Evaluate the line integral / (x+2y)dx + r’dy, where C consists of the path C from (0,0) to (3,0), the path C2 from (3,0) to (2,1), and the path C3 from (2,1) to (0,0) by applying the following steps. (a) Evaluate (x + 2y) dx + c'dy, by parametrizing C C (b) Evaluate [ (x + 2y)dx + x>dy, by parametrizing C, (c) Evaluate | (x + 2y)dx + x’dy, by parametrizing C3 (d) Evaluate (+2y)dx + xºdy
1. (5 points) Evaluate the line integral 1 + de todos dy, where C consists of the arc of the circle x2 + y2 = 4 from (0, 2) to (2,0).
Evaluate the triple integral. JJJr Oya, where is the solid tetrahedron with vertices (0,0,0), (1,0,0), (1,1,0), and (1,0,4).
Problem 1 Evaluate the line integral / x2 ds, where C is the line segment from (3,0) to (0,4) in the xy-plane.
Evaluate the integral de ryds, where C is the curve consisting of the portion of the unit circle of the cy-plane which lies in the first octant of R3, followed by the line segment extending from the point (0,1,0) to the point (-2,5,3).