Q2) Evaluates the following (Answer three only): 1) Se1 - e2xdx 73 - 3x2-4x+12 dx X-3...
Evaluate the following integrals. S 5x-2 dx x2-4 s 9x+25 (x+3)2 dx 2 x3+3x2-4x-12 dx x2+x-6
Evaluate the definite integral. (4x + sin x) dx (1) + + 73/2 (2) 12 - 2/2 (3) 212 + 2 (4) -1
Q1 dx, 115 5xita dx. 2) ſ tan°4x dx . 3) 06-341 S[cos(x? 4) + 1) + xdx, 5) prove that I cscu du = -Inlcscu + cotul + c x2 + Q2 r3 dx 1) dx 2) sino cosºede , 3) /* sec°8 de , 4) * sec`e do , 4) , Port + 4 1 5) dx . 4- x2) 4 Q3 Answer A or B (graph the functions) A-Determine the area of the region enclosed by y...
Multiple Choice: 1. Simplify "1-2x-x+5x-3x2+15+x3 a) x3-4x2+3x -1 (b) x2-4x2 +3x +1 (c) x3-4x-3x +1 (d)+4x +3x +1 2. Expand "logly' x3 a) 2(Logly)+3logx)) ( (d) 2logl)+3loglv) (b) 3log(x) 2logly) (c) 6log(x)logly) 3. quals 5 (b) 55 (c) 64 (d) 10 a) 62
1. For the following two systems of linear equations answer the questions 4 + x + 2xy + 2x - 6 3x + 2x + 3x3 + 3x = 11 2x + 2x + 3.5+ 2x- 9 2x + 2x+4x3+5x - 13 3x, +2, +4x3+4x-13 3x+3x+3x2+2x, -11 (1) Solve the above systems of linear equations using naive Gauss elimination (b) solve the above systems of linear equations using Gauss elimination with partial pivoting . Axb 2. For the following matrix...
Question 2 (Learning Outcome 2) 0 S (*x+3) dx S A) Evaluate the following integrals. 4x+7 2x+5) 5x2–2x+3 (ii) dx (x2+1)(x-1) x2+x+2 (iii) S3x3 –x2+3x+1 dx dx (x+1)V-x-2x In (x) dx (iv) S x2 X+1 (vi) S dx (1+x2) (vii) S dx x(x+Inx) (viii) Stancos x) dx (ix) 30 Sin3 e*(1 + e*)1/2 dx dx 2 sin x cos x (x) S B) Find the length of an arc of the curve y =*+ *from x = 1 to x...
2. 10 23 x · [In(x)]2 Jg x+2 In Problems 1-26, evaluate each improper integral, or show why it diverges. po 1 5 1. dx dx 2 3. dx 4. dx 13 1 + x2 5 X 5. dx 6. dx x. In(x) Jo 1 + x2 1 7 dx 8. dx -2 J3 (x - 2)2 1 1 9. dx 10. dx (x - 2) 1 11. dx 12. dx J3 (x+2)3 14 1 1 13. dx 14. dx...
3) Find the difference of quotient (**) following: f(x) = -3x2 - 4x + 2 (*),h70 for the
1 of 4 he following integrals: .nx dx (parts) 4 2) [4x² In(6x) dx parts) 3) 1x*sin2x dx (parts) 4) ſcosº x dx (trig identity) 5) ſsinº x cos*x dx (trig identity) 6) ſcosº xvsin x dx (reduction) 7) ſcot* x dx reduction) 8) ſtan x secºx dx (reduction)
8. Using Chain Power Rule a) ∫ (3X^2 + 4)^5(6X) dx b) ∫](2X+3)^1/2] 2dx c) ∫X^3](5X^4+11)^9 dx d ∫(5X^2(X^3-4)^1/2 dx e) ∫(2X^2-4X)^2(X-1) dx f) ∫(X^2-1)/(X^3-3X)^3 dx g) ∫(X^3+9)^3(3X^2) dx h) ∫[X^2-4X]/[X^3-6X^2+2]^1/2 dx