6. Review problems: Evaluate the following definite integrals: a. (3xdx . far . 2 sin (...
6.Evaluate the following indefinite and definite
integrals
6. Evaluate the following indefinite and definite integrals. (a) ſe=v2+3e* dx secat 1+tant
4. [25 points) Solve each of the following definite and indefinite integrals. Show all of your work for full credit. For definite integrals, leave numerical answers in exact form (without rounding). Please double-check to make sure you copy the problems correctly, as minor typos could change the difficulty of these substantially. a. 1(413 – 1/3 + 1)dt b. Syndx c. S x cos(3x) dx d. S 6x sin(3x) dx e. 2y In y dy
Find the following integrals: SPENT Ox (26 - secx tanx) dx 4 evaluate the following definite integrals: b) 3 sinx Cos x V 1 + 3 sinx dx let u = 1 + 3 si nax
9. (12 pts) Evaluate the following definite and indefinite integrals: (a) 12 dt d dx 1* 2 t Hint: Apply Part 1 of the Fundamental Theorem of Calculus and the Chain Rule. (b) /6 sin 20 de (sin2 @ + 2)2 -
Use the theory of residues to evaluate the following real, definite integrals: 210 do Hint: integrate on the unit circle, z = elo; dz = izdo. Hint: find the residue in the upper half plane. ſº I dx 13+5 sin e dx b. So y2 + 4x +5 J-ox? +dx
Use geometry to evaluate the following definite integrals, where
the graph of f is given in the figure.
LLLLL y=f(x) 1 1 2 3 4 5 6 7 8 x | f(x)dx
4. Evaluate the definite integrals: A) |_ In xdx 1 xV1+ ln² x I dx cos x sin x a f / Inx di -d
1. Evaluate each of the following definite integrals. a. 529,-zdy b. Sonata dx 2. Integrate. a. sec? tane de b. S tanht dt cosht
1. (34, 12) Evaluate the following integrals. For definite integrals, give answers in exact form. For indefinite integrals give your final answer in the variable x. Show work. THE WORK YOU SHOW MUST BE WRITTEN CORRECTLY. A. $()(**)dk 1. Continued. - B. -dx C. [vcosô sinº Odo
Characterize the below integrals (definite or indefinite) and solve the integrals: a. (-10x5 + 3x2 - 5x)dx b. S(-8Vx)dx C. SCEx _17) ax d. S(12e* - 9 sin x + 5x-2)dx 5 (6********=)dx