cos((+dt. (5 pts.) 1 3. Evaluate the integral 8(t)dt. (5 pts.) 4. Evaluate the sum Σ 23]n]. (4 pts.) 2 +2 +2 + 2+2 4 2
8. Evaluate each of the following. (a) L {te-t *et} (b) £{/ sin t cos(t – 7)dt
1 Evaluate the integral 6 -sin ل dt. 6 T6 -sin dt = | 한
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of the function f(x, y) = 3 sin(ry) + cos(y2) cos 5t and y(t) = 5 sin t - sin 5t for 0 < t < 2« and F is the (5) EvaluateF dr where F(x, y) with counterclockwise orientation (2y, xy2and C is the ellipse 4r2 9y2 36 _ F dr where F(r, y) = (x2 -...
(2) Apply Cauchy's Integration to EVALUATE the following INTEGRAL: 27 1 dt. 0 3 – sin(t)
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
(b) (4) Evaluate the integral 09 69 Baluate the interna sin I cos do
all
of tem
(e) sin(30) + cos(20) do 1. Evaluate the indefinite integral. (a) [8x2 – 3x2 + 3+ – 2 dr (b) 1-1 + 7x – 34" da (e) [(3+ + 2)(+ – 2) dt (8) 223/2 - 3/3+ Fadz (n) 23" +22-1 de 2. Solve the initial value problem: g'(x) = 7.76 – 4.23 + 12: g(1) = 24 3. Solve the initial value problem: W'(t) = 6 sin(3t): h() = 6
Evaluate the definite integral. ∫6 to 1 t^4 ln(4t)dt
solve 1 and 2.
Evaluate the integral. 3T/4 1) rt/4 D) o B)-16 C) Find the derivative of the integral using the Second Fundamental Theorem of Calculus 2) y- cos nt dt D) cos (3)-1 C) sin (3) B) cos (x3) A) 6x5 cos (x3)
Evaluate the integral. 3T/4 1) rt/4 D) o B)-16 C) Find the derivative of the integral using the Second Fundamental Theorem of Calculus 2) y- cos nt dt D) cos (3)-1 C) sin (3) B)...