5. (4 points) Evaluate the following integral: | (ei +: e'i + sin tj *21-, k)...
Evaluate the integral (-8 sin(t)- 4 cos() dt ntegral Evaluate the integral (-8 sin(t)- 4 cos() dt ntegral
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. (b) [20 pts] By using Stokes’ Theorem, evaluate the line integral| vi F. dr where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) [5 pts) Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts) By using Stokes' Theorem, evaluate the line integral F. dr с where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. F. dr (b) (20 pts] By using Stokes' Theorem, evaluate the line integral| " where F(t,y,z) = (y2 + cos z)i + (sin y+z)j + tk
1 Evaluate the integral 6 -sin ل dt. 6 T6 -sin dt = | 한
Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) (5 pts] Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts] By using Stokes' Theorem, evaluate the line integral F. dr C where F(x, y, z) = (y2 + cos x)i + (sin y +22)j + xk
7. (10 points) Evaluate integral ſeti + sint j + 1 k) dt. 2t-1
QUESTION 8 Evaluate the integral. dx Vx2 - 10x + 21 x-10) sin + C 2 X-5 tan +C 2 2 sin -1 X-5 2 +C x + 5 sin! + 2
(2) Apply Cauchy's Integration to EVALUATE the following INTEGRAL: 27 1 dt. 0 3 – sin(t)
need help with 5-6 In problems 5) - 8), evaluate the integral. (9 points each) 2 5) dt, At 2+1 •dt, 6) VE