Use a contour to evaluate so x²+2x da (2-1)(x3+1)
Use a contour to evaluate x? dx (x2 +1)(x2+4) f
1 Use a contour to evaluate So da 1+x4
Use a contour to evaluate S (2-1)723 +1) da 7T Answer:
2x 1 Use a contour to evaluate dᎾ (2+0 -cos)
21, 25 and ill like
In Exercises 20-38 use a contour integral to evaluate the improper integral. (22 + 1)(x2 + 4) x +3 w (x2 + 4x + 5)2 da 23. (x2 + 1)(x2 - + 1) - J-003 + 26 da
ex4.19
Ex. 4.19. Use contour integration to evaluate the following real integrals dar da (a) (b) r22x5 (x21)2 da da (c) (d) (221)(a2+4)
Ex. 4.19. Use contour integration to evaluate the following real integrals dar da (a) (b) r22x5 (x21)2 da da (c) (d) (221)(a2+4)
1. Evaluate the iterated integrals: x2+2x+y a. JR 3x+3y dA, R: 15x32,0 sys 1 (Hint: Simplify the integrand first.) b. S ey/*dA where R is the region in the xy-plane bounded between y = x2 and y = x over the interval 1sx52. c. So Sex Sx**2 x dydzdx
QUESTION 4 Use the appropriate transformation to evaluate SX (2x + y)(x - y)dA where R is the region bounded by the line y = 4 - 2x, y = 7 - 2x, y = x - 2 and y = x +1. (8 marks)
Evaluate: vr y-x dA , y + 2x+1 where R is the parallelogram bounded by y-x-2, y-x-3, y + 2x = 0, andy+2x=4.
Evaluate: vr y-x dA , y + 2x+1 where R is the parallelogram bounded by y-x-2, y-x-3, y + 2x = 0, andy+2x=4.