1. Evaluate the following: (4 points) Sr* +23 dr
5. Evaluate the integral sec" x dr. 6. Evaluate the integral I 2 dx X3 V x2 – 1 >1. 7. Evaluate the integral dc I VAI 8. Evaluate the integral 19 - 22 dc. .x2
Evaluate the definite integral. 3x2 V 23 +1dx (1) 23 V5 – 24 V2 (2) V6 - 11/13 (3) 12V7 – V2 (4) 21 V5 – ŽV7
1 dr 8. Evaluate
1 dr 8. Evaluate
Evaluate the iterated integral. 2 2 2+2 il 18 dydr dr = 18r dy dr d: = 0 0 0
COS Use a contour to evaluate dr (2° +1)
2. (20 points) Evaluate the following integral using Integration by Parts or Trigonometric Substitution dr Show all your work: i.e. If you use Integration by Parts, clearly define u,du, v, dv or if you use Trig Sub clearly define what substitution you use for r as well as dr and other corresponding parts of your substitution
Apply row operations and cofactor expansions to calculate 1 127 1 2-α -23 28 det 2 22 19 For which α is the matrix invertible?
5. Use a trigonometric substitution to evaluate Jo (2+1)3/2 dr.
Show that: (a) det(A) - (b) det (A2) [det (A)2