Evaluate the following integral using residues: cos(bx)-cos(ax) I = dx. x2 Let a and b: real...
Evaluate the following integral using residues: I = { cos(bx)-cos(ax) dx. x2 Let a and b: real constants such that a > b>0. Note: cos(bz)-cos(az) is well-behaved along the real axis (singularity at z = 0 is removable), ejbz-ejaz has a pole at the origin. Make sure to handle this point correctly 22
(b) For any real number a > 0, O COS X dx = te /a. x2 + a? - [Hint: This is the real part of the integral obtained by replacing cos x by eix]
Given the integral below, do the following. 2 cos(x2) dx Exercise (a) Find the approximations T4 and M4 for the given interval. Step 1 The Midpoint Rule says that b f(x) dx = Mn Ax[f(+1) + f(22) + ... + f(n)] with ax = . b - a + n a 1 We need to estimate 6 2 cos(x2) dx with n = 4 subintervals. For this, 1 - 0 Ax = 4 = 1/4 1/4 Step 2 Let žų...
explain please 2. Which one of the following DE is exact? a. (x+y)dx+(xy+1) dy=0 b (e + y)<x+ſe+x)dy = 0 c.(ye* +1) dx +(e' + xy) dy = 0 d. (sin x+cos y) dx +(cos x +sin y) dy = 0 e. (eº+1) dx +(e? + 2) dy = 0 3. The solution of the following separable DE xy' =-y? is a. y= '+c b. y=- c. y = In x+c In x+c d. In y=x? + e. yer+C 4....
Hi there, Here are some mathematics MCQs I needed to check my answers to. Thanks :) Question 1 x2 (In z)dr equals Select one: O a. 2 3 1 a 3++c. ob. 2+ 2ln.z 0.2.+ + c. O d. 2. (In x)2 + 2x In x +c. o e. 22 (In x)² +c. Let x, y,b and N be positive real numbers. Which of the following statements is false? Select one: a. log, (+ y) = log, I + log,...