Evaluate. Assume u > 0 when In u appears. sexy dy O A) } e4y + C B) 2e4y + C C) 4e4y + C OD) e4y + C
14.4.25 A Question Help Evaluate. Assume u > 0 when In u appears. Sie ben (Type an exact answer. Use C as the arbitrary constant.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All Check Answer
Evaluate the following integrals. (a) / In(3x) dx for x > 0 (e) / ( +er) dx (n lete* dx (e) sin(5x +1) dx
1- 2- Tutorial Exercise Evaluate the indefinite integral. Jerez 42 + ex dx Step 1 We must decide what to choose for u. If u = f(x), then du = f'(x) dx, and so it is helpful to look for some expression in Jerez 42 + ex dx for which the derivative is also present. We see that 42 + ex is part of this integral, and the derivative of 42 + ex is ex et which is also present....
13. Evaluate: (emcos x dx. Hint: Notice we see sin x and its derivative cosx. u=sin x is a good choice for substitution. 14. Evaluated as 15. Evaluate: x cos(x") sin(x)dx. Hint: Since the cosine function is taken to the 4n power, try u = cos(x).
Help please and circle the answer to the blank problem and make it clear and visible. Ive also included a similar problem so you know what the answer should look like. Thanks Evaluate. Assureu > when in u appears. (Hint: Use the properties of logarithms.) Inx? (Type an exact answer.) Evaluate. Assume u> 0 when in u appears. (Hint: Use the properties of logarithms.) x10 Substitute for In x und du for dx in the integral Inx -dx= Integrale with...
use residue theorem to evaluate the following integrals sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?
Evaluate the integral. 3 4 [ rwa f(x) dx where f(x) = 15 - x2 if -3 SXO if 0<x<3
4. (a) A particle in 1D has the wavefunction (x) = Ce-ex?12, where e > 0 and you may assume C > 0. i) Find the normalisation constant C. [4 marks] ii) For small e > 0, show that y is approximately a zero eigenvector of the momentum operator Ộ, i.e., show that lim lôy || = 0. €0+ Hint: for a > 0, recall that Se-ax?dx = Vola and Sox?e-ax?dx = Vra-312 [6 marks] (b) Let Ê be a...
Find f(x), assuming that f(x) ex dx = f(x) e' - 8x-1 ex dx. (Use C for the constant of integration.) Evaluate the integral. (Use C for the constant of integration.) cos 498(3y) sin?(3y) dy