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Integrate the following problems. Complete the strategy box to identify "u" and "du". 2 In(x) 2.8...
integrate. state du and u a) tan(4x sec (4x)dr dx r +1 b) dx x +1 c) csc (3xax a) tan(4x sec (4x)dr dx r +1 b) dx x +1 c) csc (3xax
Integrate each of the following analytically) - Using U substitution All Steps and Proper Notation MUST be SHOWN - All questions are 2 points cach 1 S 2x3 e3x* dx 2 1 272 8x dx Integrate each of the following (analytically) - Using U substitution All Steps and Proper Notation MUST be SHOWN S (1 - x)/x dx 4) SVx3 + 2 (x2) dx Integrate each of the following (analytically) - Using U substitution All Steps and Proper Notation MUST...
Consider the following initial-value problem. 5 f'(x) f(1) = 17 Integrate the function f'(x). (Use C for the constant of integration.) f'(x) dx Find the value of C using the condition f(1) = 17. с State the function f(x) found by solving the given initial-value problem. f(x) Consider the following. |--145 – 03 +49) du Simplify the integrand by distributing u to each term. SO Jau du x Find the indefinite integral. (Use C for the constant of integration.) 6...
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...
Use integration by parts to derive the following formula. ſxIn \/ dx=x** 12+Cnt=1 (n+1) If u and v are differentiable functions, then udv=uv - vdu. Let udv = x. In|x dx. Determine the best expressions for u and dv. Select the correct answer below and fill in the answer boxes to complete your answer. O A. u= O B. u= dx, dv= dv= dx Find du du= dx Integrate dv to find v. The constant of integration is not introduced...
6. Find the general indefinite integral: J (u + 4)(2u +1)du I a. (3x dx conto de ton of b. [VF (82 +31 + 2)dx cinco T() = f(x) d. Sx dx (a=-1) sin x-e' +2 de 188
Consider the following boundary value problem: du du dx dx u=-e* sin(x) Discretize the ODE using backward second-order accurate scheme for both derivatives. The second order finite accuracy difference for the derivatives are given by: 2h (3)-1(1,2)-45 (7.1)+31(x) 8 (*)== (4.5) +41 (1.2) -51 (3.1) +2f (x) h?
please solve 21 and 25 only u want to use integration by parts to find J (5.x - 7) (x - 1) 4 dx, which is the better choice for u: U = 5x – 7 or u = (x - 1) 4? Explain your choice and then integrate. B blems 15–28 are mixed—some require integration by parts, others can be solved with techniques considered earlier. ntegrate as indicated, assuming x > 0 whenever the natural logarithm function is involved....
25 &27 In Problems 15-28 find the general solution of the given higher-order differential equation. 15 y" – 4y" – 5y' = 0 16. y' – y = 0 y'' – 5y" + 3y' + 9y = 0) 18. y' + 3y" – 4y' - 12y = 0 30 d²u 19. d13 + d²u - 2u=0 dt? d²x d²x an de dt2 4x = 0 21. y' + 3y" + 3y' + y = 0 22. y" – 6y" +...
QUESTION 3 Which of the following is equivalent to x/x- 2 dx if the substitution u=x-2 is used? ºs (w/2-2012) du 5'(W12-201/2) du 1 (4312 + 20 +21/2) du O plusi2 (43/2 + 2u1/2)du