Integrate each of the following analytically) - Using U substitution All Steps and Proper Notation MUST...
USE MATLAB ONLY NEED MATLAB CODE MATLAB 21.4 Integrate the following function analytically and using the trapezoidal rule, with - 1,2,3, and 4: 0 (x + 2/x dx 0 Use the analytical solution to compute true percent relative crrors to evaluate the accuracy of the trapezoidal approximations. 0
Use only one substitution u = ... and show all the steps to find : [10] secx dx 1 - 2 sec? x
6 A Find the derivative of each of the following functions using derivative rules. Remember to SIMPLIFY first! Show all steps for full marks <2 mks each> Differentiate each of the following equations. Be sure to write proper notation. y = 7x6 + 10x4 - 8x - 5 $(x)= V1 f (x) = 7 y = 4x®(3x6 - 2x) f (x) = - s(t)= _4° +56 f(x)g(x)h(x) cf(x) f(x) + g(x)
Solve the initial value problem 2yy' + 2 = y2 + 2x with y(0) = 4. To solve this, we should use the substitution u = With this substitution, y = y' = Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. The solution to the original initial value problem is described by the following equation in x, y.
6. Prove the following trigonometric identity. Proper form is required and all steps must be shown 13 tan - X COSX-sinx cosx+sinx
Please show all steps. Evaluate the integral using a trigonometric substitution. Jo (4 – x2) 312 * - *2)3/2 dx
Evaluate the integral using the given substitution. ſ Vacos (x32-7) dx, u = x 3/2_, o x312 sin 2(x3/2 - 7)+ C o sinᵒ (8312.7) + C a o 1/3 (4x) sin (x3/2 -7)+C o $(x3/2 - 7) + sin 2(x3/2 - 7) + C
Question 4 Which of the following can be integrated by using the substitution U = In(x) S (In(x)2+1 dx. 11 Svin(x) + 1 dx. 1. S Vin(x) k IV dx. s (In(x)2 + 1 In(x) I and Ill only. II and IV only. OOO lll only ll only I and II only
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...
Evaluate the following indefinite or definite integrals using substitution. SHOW EACH STEP on the answer sheets. 16. Sa com a dx u=__ du= 17. 62 e 2 dx u=- du=