Problem 7 (5 points each) a./ (Inx) dx b. fx.ex+3dx c. ſcosx. 5sinx+3dx
Problem 1. (2 pts.) Solve: [cos d+Eco-dy Ecos xdy dx + (1 pt.) 0 COS COS Solve: dy +dx - x2dx +xdx - 3dx (1 pt.) 0
Problem 1. (2 pts.) Solve: [cos d+Eco-dy Ecos xdy dx + (1 pt.) 0 COS COS Solve: dy +dx - x2dx +xdx - 3dx (1 pt.) 0
4. Evaluate the following integrals. Show all work! (a) [r? Vx +3dx In V (b) love -dox (c) ſxv2x + ldx (d) ſtan(3x)dx
g(x)dx = 5, find the following Problem 4 (12 points). Given ( g(x)dx = 10 and integrals: (a) [(39(x) + 5x)dx (b) ["o() der
please explain the steps to your solution using Microsoft excel to
Compute the answer
7) From x-1 tox-2, find the values of the function whose derivative is dy Inx) + xy dx using the 2"d order Runge-Kutta approximation and a Ax of 0.1. At x 1, y-1.
7) From x-1 tox-2, find the values of the function whose derivative is dy Inx) + xy dx using the 2"d order Runge-Kutta approximation and a Ax of 0.1. At x 1, y-1.
5. Evaluate each definite integral. 5.2 dx 2.22 [5] /2 [5] (b) [ COS C sin? C dx 1/4
Problem # 1: (70 points) Solve the following problems (a) and (b) using Laplace Transform: a) (7 points) y(0)-y'(0)-0 y"(0)-1 b) (dX/d't) + 3 (dy/dt) + 3y-0 (7 points) (d'x/d't) +3y-te' x(0) = 0 x'(0) = 2 y(0) = 0 c) An nxn matrix A is said to be skew-symmetric if AT--A. If A is a 5x5 skew-symmetric matrix, show that 9detA)-0 (4 Points) d) Suppose A is a 5x5 matrix for which (detA) =-7, what is the value of...
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
2. If • a<b<c • Sºf(x) dx = 5 • Sog(x) = 3 • Sg(x) dx = 7 Then, what is the value of f(x) - g(x)]dx?
Problem 5 (25 points) Show that the differential equation (siny -ysinx)dx + (cosx + xcosy - y)dy = 0 is exact, and hence find the general solution. Solve the following. Simplify answers as much as possible. (a) (1+y?)dx -xydy = 0 , y(5) - 2 (b) e(sinx)dy +(e X + 1 cosx)dx = 0
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Inx Evaluate the integral. da a. 2 b. C. --- 4 d. 1 4 e. divergent Find the integral. dx x(x - 3) a. 1 X-3 +C b. 2 3 In +C X c. X 3. 3 In +C x d. X-3 3 In X Evaluate the integral. \"cos®x dx 0 a. 5 32 7 b. 3 77 16 57 c. 5 167 d. 3...