
9. Use a contour integral to evaluate the trigonometric integral. Jo 3+ 2 costat
5. Use a trigonometric substitution to evaluate Jo (2+1)3/2 dr.
Please show all steps.
Evaluate the integral using a trigonometric substitution. Jo (4 – x2) 312 * - *2)3/2 dx
(a) Use Trigonometric Substitution to evaluate the integral 22 9 dr. T (b) Use the method of Integration by Parts to rewrite the following integral. (You do not need to fully evaluate the integral.) | «* sin(x2) dr. (c) Find the form of the partial fraction decomposition of 2.r2 - 3.c + 77 (x - 1)(x² +2) (You do not need to solve for the coefficients.)
9. Evaluate o (x+ 1)2 by extending the integral into the complex plane and using the contour C shown below.
9. Evaluate o (x+ 1)2 by extending the integral into the complex plane and using the contour C shown below.
2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary of the square D = {z E C:-4 < Re(z) < 4, -4 < Im(z) < 4} traversed once counterclockwise.
3. Use the trigonometric substitution r = a sin(0) to evaluate the following indefinite integral: da
Use contour integration to evaluate the integral 2T 1 I (5 4 cos (0))2 S 0 diagram showing the contour and the singularities Draw and label a For your information, the graph of the integrand is given below. L0- 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1. 7T 2n 4. -
Use contour integration to evaluate the integral 2T 1 I (5 4 cos (0))2 S 0 diagram showing the contour and the singularities Draw and label a For...
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
(1 point) Evaluate the integral 2 Jo So tapet e godt 2 + 1 (4+3 + 12t + 3) +36 dt The integral is
Evaluate the following integral using the trigonometric
substitution method.
zu +9 dx x2