poojapattar1141

Evaluate the line integral integral_C F middot dr, where C is given by the vector function r(t). F(x, y, z) = (x + y)i + (y - z)j + z^2k r(t) = t^2i + t^3j + t^2k, 0 lessthanorequalto t lessthanorequalto 1

Evaluate the line integral integral_C y^3ds where the path C is given by C: x = t^3, y = t, 0 lessthanorequalto t lessthanorequalto 2. Evaluate the line integral integral_C F middot dr where F = (x, xy) and C is given by r(t) = (t^2, 2t) and 1 lessthanorequalto t lessthanorequalto 2.integral_C F middot dr =

Given F(x, y) = (2x + 3y)i + (3x + 4y)j Find a function f(x, y) satisfying f(x, y) = F(x, y) Use the fundamental theorem to compute the line integral integral_C F middot dr along a curve C from (1, 0) to (1, 2) Evaluate integral integral_E integral xyz dV where E = {(x, y, z) | 1 lessthanorequalto x lessthanorequalto 2, 0 lessthanorequalto y lessthanorequalto x, 0 lessthanorequalto z lessthanorequalto y}

Find the gradient field F of the function f. 1) f(x, y, z) = x^4 x^8 + x^8/z^3 Evaluate the line integral of f(x, y) along the curve C. 2) f(x, y) = x^5/squareroot 1 + 4y, C: y = x^2, 0 lessthanorequalto x lessthanorequalto 3

Evaluate the line integral of f(x, y) along the curve C. f(x, y) = x, C: y = x^2 0 lessthanorequalto x lessthanorequalto squareroot 15/2 63 21 63/8 21/4

Evaluate the line integral of f(x, y) along the curve C f(x, y) = 3y^2, C: y = e^-x, 0 lessthanorequalto x lessthanorequalto 5