I use residue theorem to solve this problem
please prove part (b) use complex analysis and calculus of residue -dx neif a> 0 5. (a) x2+1 (b) For any real number a > 0, cos x dx ne"/a. a Hint: This is the real part of the integral obtained by replacing cos x by e
Evaluate the following integral using residues: cos(bx)-cos(ax) I = dx. x2 Let a and b: real constants such that a > b >0. Note: cos(bz)-cos(az) has a singularity at z = 0 is removable, z2 ejbz-ejaz has a pole at the origin. Make sure to handle this point correctly 22
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
Use logarithmic differentiation to find dy/dx. y = XV x2 + 25 X>0 dy - dx Need Help? Read It Talk to a Tutor
Suppose f is continuous, f(0)=0, f(2)=2, f'(x)>0 and f (x) dx = 1. Find the value of the integral fro f-?(x) dx =?
Evaluate the integral. 3 4 [ rwa f(x) dx where f(x) = 15 - x2 if -3 SXO if 0<x<3
State the quadrant in which lies. sin(8) <0, cos(8) < 0 OII III OIV 8 If sin() and 8 is in the 1st quadrant, find the exact value for cos(8). 9 cos(8) - > Next Question State the quadrant in which lies. tan(8) > 0, csc(8) < 0 01 OII O III OIV
(1 point) If f(x) = { 6x, x39 8 x >9 Evaluate the integral 10 6.". f(x) dx |
All work please Evaluate: SỐ 9(x) dx, where g(x) = x2 for x 5 2 = 5 + x for x > 2 Find the average value of y = 4x3 + 2x over the interval [–2, 1]
Let T: P2 --> R2 be the linear transformation such that T(x+1)=(1,1), T(x2)=(1,0) and T(x-1)=(0, 1). Find T(2+x+x2).