1 + V9 – x2 if – 3 < x < 3 Define f(x) = the graph of which is shown below: if x > 3 3 2 1 -1 2 6. .5 culate f(x) dx using geometry and any integration properties or techniques. (You may use any relevant antiderivative formulas.) -3

Q: Q-4) Find the integration of function (f (x) = x2 + 1) by using "Simpson Rule" when (n=6) on the…

A: Simpson's rule is used to approximate the definite integral which represents the area under the…

Q: If the change of variables u=x²+4 is used to evaluate the definite integral f(x) dx, what are the…

A:

Q: Q9/ find the integration ſe^( (2x) ^3-1) x2 dx? * 1 а- 6. e2x* -1+c 1 b- e2x3 +C 1 .2x3–1+

A:

Q: Now solve the boundary value problem: A" (y) - X² A(y) = S(y-E), 0<<Y₁] A'(0) = A'(Y) = 0, 0<<Y}}…

A: Given That : A"(y)-λ2A(y)=δ(y-ξ),  0&lt;ξ&lt;Y, A'(0)=A'(Y)=0 To Find : solve the boundary value…

Q: 2. Given So S√x y² +8 dydx. Reverse the order of integration and evaluate. Draw the

A:

Q: 2 Example 10.8. Using Euler's method, find an approximate value of y corresponding to x= 1, given…

A:

Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

A:

Q: 1. Evaluate the indefinite integral (a) S (e2× +– 3) dx (b) S(4x³ + Vx)dx 2. Find the function f(x)…

A: We will use the formula ∫eax dx= eaxa∫xndx = xn+1n+1∫1xdx = ln(x)   Hence 1) a)  ∫e2x+2x-3dx =…

Q: 15x²x³43x - 19 The integral f S can be rewritten as (x + 1)²(x² - 6x + 13) Ax + B C D Slax + + ax² +…

A:

Q: find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

A: Given:- function y=x2-8 Inxdefined on the interval 1, 5 The derivative of the function is y'=2x-8x…

Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of x²+bx+ca -dx? 3 A…

A: This is a problem related to integration. Based on the concept of partial fraction decomposition we…

Q: Q 3. Test the exactness of ODE, if not, use an integrating factor to make exact and then find…

A: It is linear differential equation.

Q: 1 (a) Evaluate the integration of the following functions: x 2 +2 (i) (ii) fx*e*. dx

A:

Q: Let : 6e* – 8. Find x (t) such that dt x(0) = 5. Round any numbers to 4 decimal places if necessary.…

A:

Q: 3. Find the Valuo OF C Conkinous at X=1 which makes tho Following Function (メー30-1, X<1 キ)= 3C cos…

A: Solve the following

Q: Q1 (a) Integrate the following definite integrals using suitable method: (i) S, tan-1 x dx (ii) a dx…

A: To evaluate the given integral

Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: 4 dx Vx(1 + x) roper for two reasons: The interval [0, co) is infinite and the integrand h 4 4 dx =…

A: Here we use substitution so simplify the integration.

Q: A function is approximated by a cubic spline defined by: 25/12 30.0833 An approximation of ff(x)dx…

A: Sol:- Consider the function in the range of (0,1) ∫011+x+x2+x3dxApply the Sum Rule:…

Q: 8) A rational function has a HA at y = 2, an x -int of a VA at x = -4 and a y-int of - 3 Determine…

A: Given that the VA is x=-4, this means the denominator has a factor= (x+4) Given that the x-int is…

Q: 51. The functions y = e* and y = x³e do not have elementary anti- derivatives, but y = (1 + 3x)e"…

A:

Q: Q1/ -Evaluate 1- x3 Vx2 + 1 dx by using integration by parts 1 Add file re 2ln10 log10 x 2- S. dx 1…

A:

Q: 6 1) Find the general antiderivative for f(x) = 1+ x?

A:

Q: Q2: Find the value of the following integration, using : 1- Two-points Gaussian integration method.…

A:

Q: 90% of it Suppose dy/dx = x-y and y = 2 when x 1, Use Euler's Method with increments of Ar = -0.1…

A: Given the differential      dydx=x-y with y(1)=2. Find y(0) using Euler's method with step size…

Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: If the change of variables u = x + 1 is used to evaluate the definite integral f(x) dx, what are the…

A:

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: 6. Use Methods of Integrating factor to solve the DE below: dz + 2 xz = 2 e-x? a) dx dy b) x 2- 2 y…

A:

Q: Q6: Use classical fourth-order RK method to solve the following problem over the interval from x= 0…

A:

Q: 3. Evaluate the definite integral. Give exact answers S(x² + 2x – 4)dx - a. ~2 2x+1 dx Vx2+x-2 b.

A: Take integration. Follow step 2nd .

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: 3. The integration of x e* with respect to x is: A. e2x. В. 2хе* С. 2

A: To integrate  xex2 with respect to x: ∫ xex2dx Apply u-substitution: u=x2 Differentiate both sides:…

Q: 5) [xe*dx (Use Integration by Parts) 6) If [g(x)dx = (8x“ + 2)* +C, find g(x).

A: We will use integral by parts to solve the first given question and differentiation to solve the…

Q: 3. (1−x³) d²y dx² DE -+ (sin x)y' − 3xy = ln x(+1) TYPE ORDER DEGREE LINEARITY

A: Need to write down the type, order, degree and linearity of the given differential equation.

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: 1. Use integration by parts to prove the reduction formula S(Inx)" dx = x(lnx)" – n S(Inx)"-1dx. %3D

A:

Q: 5- Find the tangent (slope) of the function f(x) = x3 - 6x2 + 12x +8 when x = 6- Find the results of…

A: Since question 6 is graded so as per company's rule, i can't answer any graded question. So i answer…

Q: Q3. A) Test the continuity of the function f(x): F(x) = 3- x 2 <x <3 3< X < 4 X = 4 X +1 2х -1 B)…

A:

Q: 5. The integration form of , XY dA where Dis the portion of x+Y = 2 in the 1" quadrant will be

A:

Q: Define (1 + V9 – x² if – 3 3 the graph of which is shown below: 5 1 -2 -1 3 6. 7 5 Calculate f(x)…

A: Given,  fx = 1+9-x2 if -3≤x≤319x2if x &gt; 3  We have to find ∫-35fxdx.

Q: x³ dx Using integration by parts to solve f √4- and letting U = - then v = f(x) is

A: Topic:- function and integration

Q: 3(b) Find the indefinite integral of S*vx+6 dx

A: We need to find integral.

Q: Given the initial conditions y=1 at x-1, estimate y at x=1.2 using a stepsize h=0.1. Use…

A:

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: Find the value of the constant C for which the integral 5x 5C dx 2 X² + 1 Зх + 1 converges. C = 3…

A: Convergence of integral

Q: 1. Use algebraic manipulation and (if necessary) u-substitu- tion to integrate the function. (a) /…

A: Hey, since there are multiple questions posted, we will answer the first three subparts of the…

Q: 1+x Find the approximation of dx using Simpson's rule with step size h = 1+x2 0.25.

A: Simpson's rule: numarical methods

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.