1. Evaluate the following integrals: (1) SH/2 V1 + cos x 1 J-1/4 1+sin x 2...
3. Evaluate determinants of (SH cos no sin nel 1-sin no cos nel 114 | 2 15 2 51 o 8 8 -21
4. Evaluate the definite integrals: A) |_ In xdx 1 xV1+ ln² x I dx cos x sin x a f / Inx di -d
DO NOT use a calculator. Exact answers only, no decimals. 1. (10 pt each) Evaluate the following integrals: since) dz In(In(x b. dr c. cos(x)(sin(a)2 dz d.2tan (') dr 1. (10 pt each) Evaluate the following integrals: since) dz In(In(x b. dr c. cos(x)(sin(a)2 dz d.2tan (') dr
Evaluate the following integral. 1/2 7 sin ?x -dx 1 + cos x 0 1/2 7 sin 2x dx = V1 + cos x 0 Score: 0 of 1 pt 1 of 10 (0 complete) HW Score: 0%, 0 of 10 pts 8.7.1 A Question Help The integral in this exercise converges. Evaluate the integral without using a table. dx x +49 0 dx X2 +49 (Type an exact answer, using a as needed.) 0
4. Use integration by parts to evaluate the following integrals. (a) [(x +3) (x+3) sin(2.c) d.c (2.5 - - 1)e" dx In (2.c) d.
4. Use an appropriate substitution to evaluate the following integral: 3/4 cos(V1 – x (1 – x dx 0
use residue theorem to evaluate the following integrals 16) cosa 30 de 5- 4 cos 20 17) COSI det (x + 1)? sin 3x dx 18) sin x dx (x² + 4x+5 19)
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
use residue theorem to evaluate the following integrals sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?
1 φ.c(Sh<) Cos Csin 2r) 3. sinCcos ) 4. Sin CCos 20) Cos' Csines) 2 , 1 φ.c(Sh