Integration by Parts
∫(lnx)dx
xlnx - x + c
∫(x+14)/(x+5)(x+2)dx
-3ln|x+5| + 4ln|x+2| + C
Let y=f(x) be the solution to the differential equation dy/dx = 2x + y with initial condition f(1)=0. Approximate f(2) using Euler's method with 2 steps of equal length, starting at x=1
3
1∞∫(1/x3)dx
1/2
∫(3xe^3x)dx
xe^3x - 1/3e^3x + c
Free 200 Points
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Let y=f(x) be the solution to the differential equation dy/dx = x - y with initial condition f(1) = 3. Approximate f(2) using Euler's Method with 2 steps of equal length starting at x=1
7/4
01∫(1/x1/2)dx
2
∫(sin^-1(x))dx
xsin^-1(x) + (1-x^2)^1/2 + c
∫((x-2)/(2x+1)(x+3))dx
ln|x+3| - 1/2ln|2x+1| + C
Let y=f(x) be the solution to the differential equation dy/dx = x + y with the initial condition f(1) = 2. Approximate f(2) using Euler's Method starting at x=1 with a step size of 0.5.
6
0∞∫(1/(x+1)2)dx
1
∫(x^4)(sinx)dx Hint: Tabular method
-(x^4)(cosx) + (4x^3)(sinx) + (12x^2)(cosx) -(24x)(sinx) - (24cosx) + c
∫((3x+1)/(x2-x-6))dx
2ln|x-3| + ln|x+2| + C
Let y=f(x) be the solution to the differential equation dy/dx = 2x - 2y +3 and y(3) = k. Using Euler's Method, starting at x=3 with a step size of 1, gives the approximation y(4)≈-6. What is the value of k?
k = 15
0e∫(ln x)dx
0
∫(lnx/x^10)dx
-lnx/9x^9 - 1/81x^9 + c
∫((4x2-7x-12)/(x)(x+2)(x-3))dx
2ln|x| + 9/5ln|x+2| + 1/5ln|x-3| + C
Let y=f(x) be the solution to the differential equation dy/dx = 3x - 2y with the initial condition f(0) = k, where k is a constant. Using Euler's Method, g(2)≈4.5, starting at x=0 with a step size of 1. What is the value of k.
k = 1.5
Free 500 Points
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