MATH 201 Lecture Notes - Lecture 1: Qi

4. Integrate fox, y, z) V +y over the involute curve r(t)-(cost + t sint)i + (sin t-t cost)j, 0 t V3. h 2 paths join r2+ y

Consider F and C below. F(x, y)i 2y arctan(x) j 1 + X c: r(t) = t2 i + 3t j, 0 t 1 (a) Find a function f such that F = Vf f(x, y) = |y?arctan(x) 2 (b) Use part (a) to evaluate V. dr along the given curve C.

Find a vector equation for the line through the point P = (1, -2, -5) and parallel to the vector V = (-2, 2, -4). Assume r(0) = li - 2j - 5k and that V is the velocity vector of the line. r(t)= I + j + k