(1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t). (1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t).
18. Evaluate the following: S“ 1 - cos 30)de
(1 point) Use the chain rule to find du dt where w = x+y4 + y 25, x = e', y = e' sint, z = = e cost First the pieces oho д ㅋㅋ Thu d Now all together Bu da dt er de Che dy y de is too horrible to write down (correctly). 3: di
1. Calculate the definite integral 1 (229-33 +5) de (a) Find an antiderivative F(x)= (b) Evaluate F(2) F(2) = (c) Evaluate F(1) F(1) = (d) Calculate the definite integral 3x + 5) dx = 2. Calculate the definite integral. Give exact answers. Зе -Te du (a) Find an antiderivative F(*) = (b) Evaluate F(0) F(0) (c) Evaluate F(-1) F(-1) = (d) Calculate the definite integral.
(a) Evaluate | SL via de dy ds. e dadydx by using cylindrical (b) Evaluate the iterated triple integral coordinates.
(1 point) Evaluate the integral I va tit va de Note: Use an upper-case "C" for the constant of integration.
Evaluate the following integrals... (1 point) Evaluate the following: a. 1 (8 + e-t) $(t – 4) dt = J-1 (6 | (8 + e +) 8(t – 7) dt = . %8+*80) dr = (8 + e +) 8(t) dt = 00
(j) ſte tanº e de Hint: Etan2 e. Bonus Questions 1. (2 points) Evaluate the definite integral 2-2 dx as a limit of Riemann sums. Hint: take the sample points x* = Xi-1Xi, i = 1, 2, ..., n. The idea behind partial fractions might also prove helpful. 2. (3 points) Develop a technique of integration using the Quotient Rule (in the same way that the Chair Rule was used to develop the Substitution Rule and the Product Rule was...
(1 point) Evaluate the definite integral. | << + 1)e+2+28-3 dx =
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