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dr J0 3. Let a be a positive constant such that a 1. Evaluate the definite...
1. Evaluate the following definite integral using the substitution formula: LI 4 cos(x) sin(x)dr.
1. Evaluate the following definite integral using the substitution formula: LI 4 cos(x) sin(x)dr.
Problem 4 A definite integral I is given as .b I=| f(x) dr a=0 b=2 f(x) = e-r' ; ; ; Evaluate the...
Problem 4 A definite integral I is given as .b I=| f(x) dr a=0 b=2 f(x) = e-r' ; ; ; Evaluate the integral using the three-point Gaussian quadrature method Solution:
Problem 4 A definite integral I is given as .b I=| f(x) dr a=0 b=2 f(x) = e-r' ; ; ; Evaluate the integral using the three-point Gaussian quadrature method Solution:
#2 #3 #4 please snf thank you :) Evaluate the following anti derivatives (Indefinite integral) 1)「(2x3-5x + 7)dr 3 x ax Evaluate the following definite integrals: 01 2Sec2xdc Evaluate the fo...
#2
#3 #4 please snf thank you :)
Evaluate the following anti derivatives (Indefinite integral) 1)「(2x3-5x + 7)dr 3 x ax Evaluate the following definite integrals: 01 2Sec2xdc
Evaluate the following anti derivatives (Indefinite integral) 1)「(2x3-5x + 7)dr 3 x ax Evaluate the following definite integrals: 01 2Sec2xdc
(j) ſte tanº e de Hint: Etan2 e. Bonus Questions 1. (2 points) Evaluate the definite...
(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...
please 2 only, thanks Exercises dA (1) Use Cauchy's residue theorem to compute Jo 2+sin (2)...
please 2 only, thanks
Exercises dA (1) Use Cauchy's residue theorem to compute Jo 2+sin (2) Repeat the preceding exercise for 8" 131. (3) Let a be a complex number such that lal < 1. Prove that (2 27 Jo 1 - 2a cos 0 + a2d6 = 1 - 22 (4) What is the value of the integral in the preceding exercise when |al > 1? (Hint: Let b= 1.)
2. (a) Sketch the region of integration and evaluate the double integral: T/4 pcos y rsin...
2. (a) Sketch the region of integration and evaluate the double integral: T/4 pcos y rsin y dxdy Jo (b) Consider the line integral 1 = ((3y2 + 2mº cos x){ + (6xy – 31sin y)ī) · dr where C is the curve connecting the points (-1/2, 7) and (T1, 7/2) in the cy-plane. i. Show that this line integral is independent of the path. ii. Find the potential function (2, y) and use this to find the value of...
(1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r ...
q2 please
(1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r and y. (2) Let f,g : R → R be functions of one variable such that f" and g" are continuous. Show that (f"(x)-g"(y)) dydx = f(0) + g(0)-f(2)-9(2) + 2f'(2) + 2g'(0). o Jo (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2acos φ for 0 φ 1. Find the...
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3), 0StS 4 Evaluate F. dr Justify...
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3), 0StS 4 Evaluate F. dr Justify your answer. iii. Find a function y: R3-+ R such that F iv. Evaluate F.dr where「is the path y =r', z = 0, from (0.0.0) to (2.8.0) followed by the line segment from (2,8,0) to (1,1,2) 22 marks)
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3),...
Problem 4 (a). 1 Evaluate dx, where i is some positive constant. -5teis +6e-ix Problem 4...
Problem 4 (a). 1 Evaluate dx, where i is some positive constant. -5teis +6e-ix Problem 4 (b). Given that f(x) is continuous everywhere and 7/4 f(2 sect) dt =1010, cost 0 evaluate ) (/*+2+ +5 )dt. --1 Problem 4(c). Let f(x) be continuous on (0,1). T T Show that Į 2 f(sin x)de = / f\sin x)dz. 0 0
1. Evaluate the following definite integral using the substitution formula: LI 4 cos(x) sin(x)dr.
Problem 4 A definite integral I is given as .b I=| f(x) dr a=0 b=2 f(x) = e-r' ; ; ; Evaluate the integral using the three-point Gaussian quadrature method Solution:
Problem 4 A definite integral I is given as .b I=| f(x) dr a=0 b=2 f(x) = e-r' ; ; ; Evaluate the integral using the three-point Gaussian quadrature method Solution:
#2
#3 #4 please snf thank you :)
Evaluate the following anti derivatives (Indefinite integral) 1)「(2x3-5x + 7)dr 3 x ax Evaluate the following definite integrals: 01 2Sec2xdc
Evaluate the following anti derivatives (Indefinite integral) 1)「(2x3-5x + 7)dr 3 x ax Evaluate the following definite integrals: 01 2Sec2xdc
(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...
please 2 only, thanks
Exercises dA (1) Use Cauchy's residue theorem to compute Jo 2+sin (2) Repeat the preceding exercise for 8" 131. (3) Let a be a complex number such that lal < 1. Prove that (2 27 Jo 1 - 2a cos 0 + a2d6 = 1 - 22 (4) What is the value of the integral in the preceding exercise when |al > 1? (Hint: Let b= 1.)
2. (a) Sketch the region of integration and evaluate the double integral: T/4 pcos y rsin y dxdy Jo (b) Consider the line integral 1 = ((3y2 + 2mº cos x){ + (6xy – 31sin y)ī) · dr where C is the curve connecting the points (-1/2, 7) and (T1, 7/2) in the cy-plane. i. Show that this line integral is independent of the path. ii. Find the potential function (2, y) and use this to find the value of...
q2 please
(1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r and y. (2) Let f,g : R → R be functions of one variable such that f" and g" are continuous. Show that (f"(x)-g"(y)) dydx = f(0) + g(0)-f(2)-9(2) + 2f'(2) + 2g'(0). o Jo (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2acos φ for 0 φ 1. Find the...
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3), 0StS 4 Evaluate F. dr Justify your answer. iii. Find a function y: R3-+ R such that F iv. Evaluate F.dr where「is the path y =r', z = 0, from (0.0.0) to (2.8.0) followed by the line segment from (2,8,0) to (1,1,2) 22 marks)
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3),...
Problem 4 (a). 1 Evaluate dx, where i is some positive constant. -5teis +6e-ix Problem 4 (b). Given that f(x) is continuous everywhere and 7/4 f(2 sect) dt =1010, cost 0 evaluate ) (/*+2+ +5 )dt. --1 Problem 4(c). Let f(x) be continuous on (0,1). T T Show that Į 2 f(sin x)de = / f\sin x)dz. 0 0
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