


1. Evaluate each of the following definite integrals. a. 529,-zdy b. Sonata dx 2. Integrate. a....
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
1. Evaluate each of the following indefinite integrals. 6 Idx b. S [2 cost – 5 sin t]dt x*- x -dx c. d. I cotx sec?x dx
6.Evaluate the following indefinite and definite
integrals
6. Evaluate the following indefinite and definite integrals. (a) ſe=v2+3e* dx secat 1+tant
need help with these two please
3. Evaluate the definite integrals: a. L2x dx b. 4. Evaluate the definite integral: 5x2(4x3 – 2)* dx $ 5x(4x2 -
Problem 2. Evaluate each of the following integrals. a) In(4x) dx 1 4x+1 dx ex b) Jo c) S (5x-2)e 6x dx
10. (26pts) Find each of the definite integrals, indefinite integrals, and derivatives. 2 dx .22 5) / see?zda (7 - cos x) dc (d) dc sin (x2 – 4) dt (e) ["47" (3+z")" dx () /22"/+ 2 du
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
4pm 29.pd 1. Evaluate the definite integrals, * dx 2. Use an integral to find the shaded area below etx=h
Use the properties of the definite integral in your solutions. 1. Suppose that [*r(e)dx = 5, [° f(a)dx = -3, [*9(a)dx = -1, and ſº o(e)dx = 2. Evaluate Jo each of the following definite integrals. (a) %* ((e)+ 9(e) de (b) [" (F(*) + 9(a) do (e) ſ (sca) – ola) de (a) " (45(e) – 39(a) de