Determine the general antiderivative of the function. 1 8 (x) = %3D 1+4x² True or false? S (x) = ; · arctan(2x) + C

Q: Solve the IVP d3 t3X(t) - 9x(t) = 18 e-3t dt x(0) =8 x'(0) = 9 x"(0) = 0 then find x(0.5) accurate…

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Q: Whch of the futowing tunction is a iner tunctiont Sx)- V3x -4 S(x) = x +5 O oton O outen f(x) = 2x…

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Q: Q3\ using Euler method, find an approximate value of y corresponding to x€ [0 -0.7], Given = x(x +…

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Q: 2.) Find the critical values for g(x) = x?e-2x %3D

A: Critical points are the points at which derivative of function is zero or function is not…

Q: 2x +1 The antiderivative of f(x) is (x – 3) (x – 2) A F (x) = 5 ln x – 3 + C x – 3 7 x - 2 B None of…

A: Here we have to find the antiderivative of the given function f(x).

Q: Q.2 Evaluate I = f* x*(1 - √x) dx using Beta-Gamma functions.

A: Given: Integral I = ∫01x4(1-x)5dx We have to evaluate the given integral using Beta Gamma function.

Q: VX-2 H Evaluate dy/sx if O y=1X+1)“ Szx-1 at x=\ V(X+3)3 atメ=1 at X-3

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Q: Find the function with deriative f' Ga) = e5x tht through passes %3D the point P=(o,4/5)

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Q: 3(x² + y²)dx + x(x² + 3y² + 6y)dy = 0 a.x³e²y + 3xy²e2y = C 5.x³ev + 3x²y²e° = C c.x³e2y + 3xy²e²y =…

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Q: valuate the given function yln x In y dx + dy = 0 1. xlnx + In(lny) = x + C 2. xlny + In(lnx) = x +…

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Q: Find an antiderivative of the given function. 28

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Q: 28. Evaluate eš dx and determine its particular antiderivative whose x-intercept is ln 3. 1 e3x – 3…

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Q: 15. If g(x) and h(x) are both antiderivatives of some func- tion f(x), then what can you say about…

A: Consider that gx and hx are both antiderivative of function fx. Find gx-hx.   Since gx and hx are…

Q: 1 (2) Suppose that g(x) is an antiderivative of and g(1) = 3. 2 Va3 What is the value of g(4) ?

A: Given:        Let fx=-12x3     g(x) is the anti-derivative of f(x).       By anti-derivating  the…

Q: B. Solve the following using Integrating Factor by Inspection. Except when exercise indicates…

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Q: Determine the antiderivatives of the following functions: 1. V1-4x² dx 12 2. 1+9x² dx 3. 4+(x-3)² dx

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Q: The integrating factor of the given DE are already given below. What is the value of "n" y(y²-x-6)dx…

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Q: dy Solve the initial-value problem for y as a function of x. (49 – x²). dx = 1, y(0) = 4 Y =

A: We will solve this integration using trigonometric substitution as follows

Q: 10. The integrating factor of the FOLDE y'-2xy x is e^(-x^2) I am Sorry !!!!

A: The given differential equation can also be written as dydx-2xy=x Since it is a first-order linear…

Q: xy + e^y = ln(x + y) defines y as a function of x implicitly for the most part. Express dy/dx in…

A: Given an equation, Where y is a function of x.

Q: 7. Find the most general antiderivative of the function 9 (z) = - z² +1

A: We use Trigonometry substitution to find anti derivative

Q: ... : S (1 + 2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = 2 f(x)dx, then the…

A: Given is  ∫0∞(1+2x)e-xdx u=-1-2x, dv=32f(x) dx Integration by parts formula is ∫udv=uv-∫vdu.

Q: 10u +4 /ũ Find the most general antiderivative of f(u)

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Q: 44. Solve for the second derivative of y = e5x а. 25е5x b. 25e4* c. 25e3* d. 25e2x 45. Find dy/dx of…

A: NOTE: Refresh your page if you can't see any equations. . take derivative take the second…

Q: Q.4 Find the most general antiderivative of the function 1) f(x) = 2x + 1 2) f(x) = cos2x + sin3x…

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Q: x³dx =², then = f(x) is Using integration by parts to solve and letting u = V4-x2

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Q: If P(x) = -1/x then the integrating factor is a. e-* 1 b. С. -x d. e-1/x

A: Consider the linear differential equation: dydx+pxy=qx The integrating factor for above linear…

Q: |1+x (a) Find the approximation of ſ dx using Simpson’s rule with step size h = 1+x2 0.25.

A: We need to find ∫011+x1+x2dx using Simpson's rule using step size h=0.25 f(x)=1+x1+x2 The value of…

Q: Find a positive constant that satisfies the equation: ∫(1/x²+a²)dx=1    integration limits: [ 0,…

A: Consider the equation ∫0∞1x2+a2dx=1 We have to find the value of a Use integral formula…

Q: Г. 5 1, г)ах — 9, g(x)dx 8 Compute: -[о g(x)dx b.) == 5 3f(х)dx %— с.) .5 f(x)dx d.) 2 "/Г 5…

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Q: If G(x) is an antiderivative of g(x) and F(x) = G(x)- 5, then F(x) is also an antiderivative of…

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Q: If µ(x) ef (x) is an integrating factor of linear D. E x y' + xf(x) y = x* y – x² sin x where f' (1)…

A: To find - If μx = efx is an integrating factor of linear D.E. x3y' + xfx y = x4y - x2 sinx, where…

Q: 4. Use variation of parameters to find a general solution of r'y" + 5a?y" + 2:ry/ – 2y = x³ log(x)

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Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

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Q: * The solution of | x + 3| = 4 is :18 7 or 1 O 1 or -7 O 7 O the integration of the function below…

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Q: The expression 2xy³ is an integrating factor for x²y³dx + x(1+ y²)dy = 0. A) True B False

A: The given differential equation is  x3y3dx+x(1+y2)dy= 0  We have to check that 1/2xy3 is integrated…

Q: 4. (a) dzy Solve: dx2 + ( = 0. (b) Solve xy" + (1 – x)y' – 2(1+x)y = e-*(1 – 6x) by the method based…

A: We have, d2ydx2+dydx+dydx3=0 ..i Put dydx=v ⇒d2ydx2=dvdx Now substitute in equation i we get…

Q: x² – 25 S The antiderivative of dx is V x2 – 25 – sec-lx+ C. A True В False

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Q: Q3\ using Euler method, find an approximate value of y corresponding to X€ [0 -0.7], Given = x(x +…

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Q: Solution of+=e* using integrating factor is dy dx y= xe* + et y=xe*-e* −c x X Option 1 O

A: The given equation is;  dy/dx +y/x =ex.

Q: 6x 29. What is the particular antiderivative of f(x) = whose y-intercept is –4? 1 a. y = 4 ln |x² –…

A: We have to evaluate the above integrals.

Q: -8 dx c – 2)(x² + 4) an upper-case "C" for the constant of integration.

A: We use partial fraction to find integral

Q: A. By simple integration rules 1. fki+3x-2 + 5x+)dx 2. s**-5x²+4x dx (x-1) 3. S*- x3 -343 dx X-7 4.…

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Q: Lec 4.1: e Js Estimate with n Hhe aceuracy of 10t Brsection' Method and decidny applyning on b. De…

A: We can form a function f(x) for approximating square root of 5 then we can use bisection method.

Q: 16 Suppose we know that (3fx)-2)dr-6 4 and that Sxf (x²) dx =8. ise this information and properties…

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Q: Consider the function f(x) = 3x? + 10x – 3. f(x) has a critical point at z = A. Find the value of A:…

A: The function f(x)=-3x2+10x-3

Q: An integrating factor of y+ x+ xy² dx+ x* |dy = 0 is 3 2 4 1 A) B) x3 1 C) - D) x2

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Q: 2.) Find the critical values for g(x) = x?e-2a %3D

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