4.2 Apply the appropriate method to calculate the following: x5+ I = S = s** dx x2 -4

Q: 2. Evaluate the integral 4 dx V2x-5 5/2

A:

Q: Find the length of the graph of y = (1/2) cosh 2xfrom x = 0 to x = ln 25.

A: Length of the graph y=f(x),a<x<b is given by L=∫ab1+dydx2dx Here,  y=12cosh 2x⇒dydx=122sinh…

Q: Assume that your computer completes a 5000 equation back substitution in 0.005 seconds. Use the…

A: Given: The computer completes a 5000 equation back substitution in 0.005 seconds.

Q: 3. (a) Determine S 2xe3*dx by using integration by parts.

A:

Q: 4 a) Integrate S x3 sin ( x3 – 8 ) dx

A: Given: I=∫x13sinx43-8dx For evaluating given integral, we substitute x43-8=t…

Q: By Simpson's method, find an approximation for [(x³−2x³)dx_(n=4) 0

A: What is Simpson's Rule: Simpson's rule is a tool to approximate an integral. It is the process to…

Q: Integrate: dp 16 + p?

A:

Q: the metrod of variation of parameters to Apply Solve my = Secnn dx2

A:

Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate I = In(2 +3/x) -dx, 12…

A: To use the composite Sympsopns 1/3 rule with step length h=0.4.

Q: 4) Evaluate the definite integral: S, (6x² – 3x + 7)dx.

A:

Q: 6. Evalvate the Integral S13 sec O tan? o do =

A: ∫13sec4θtan2θ dθ

Q: The approximation of xln(x + 3) dx using two points Gaussian quadrature formula is:

A:

Q: Use Euler's Method with an appropriate h value of your choosing to estimate y(4) with y = 0.5, y (1)…

A: Topic- Differential Equation

Q: 2 Evaluate the integral S (3x³ – 2x² + x) dx. 1

A: We solve it by integrating polynomial

Q: 2. The rate at which the total average of COVID cases is dz increasing at r = 10 tents and than if…

A: If 30 tents are built, the average number of COVID cases per tent will be 7 cases while the average…

Q: 4) Evaluate the definite integral: S, (2x² – 4x + 6)dx. -

A:

Q: Suppose X1, ..., Xn are iid with PDF f (x | 0) = 40ªx-5. x > 0, where 0 > 0. Find the method of…

A:

Q: 1 7. Evaluate the integral -dx using Simpson's method and also find the error comparing ó x +9 with…

A:

Q: 1/2 x3 dx 1- V3 - 15 15 2 16 Option 1 Option 2 1 15 V15 16 8. Option 3 UOption 4 IN

A:

Q: 19. Give the midpoint approximation of xdx with n = 2.

A: Here, to approximate the given integral ∫04x3dx  using midpoint approximation with n=2. Let, f(x)=x3…

Q: The rate at which the total average of COVID cases is dr increasing atr= 10 tents and = 1 tent per…

A: If 30 tents are built, the average number of COVID cases will increase by 7  while the average…

Q: 3,2 Evaluate the integral xx + x +2 dx%3D

A:

Q: find the general slühion with real values fn +y(H)=0

A: I am consedering y4(t) to be (y'(t))4

Q: If UX = 6 and XY = 5 solve for UV. Round to the nearest %3D %3D hundredth. U

A:

Q: 5. Find the integral 1 -dx x -5x +6

A:

Q: 1. Evaluate 5 S Sx (x + 3x)dydx

A: Given, ∫05∫0x x(x + 3x) dy dx=  ∫05∫0x (x2 + 3x2) dy dx=  ∫05 ∫0x (x2 + 3x2) dydx= ∫05 ∫0x 4x2 dydx

Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) -dx, 9• I = 1+x²

A: Given: I=∫26 ln(2+3x)1+x2dx

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

A:

Q: Use Euler's method to calculate the first three approximations to the given initial value problem…

A: answer of given question is in step 2

Q: •2 5. Calculate | x In(3x)dx.

A: Given integral:

Q: 8. Approximate the value of xIn(x+1)dxusing left endpoints with n-4. Round to three decimal places.

A: We have to approximate given integral.

Q: Part 7 Give the appropriate trig sub that would be used to evaluate dr. Do ΝΤ x² – 16 solve the…

A: The given integral is ,∫x3x2-16dx Now we can use trigonometric substitution as, x=4secθ it gives…

Q: Solve the nonhomogeneous opdr – 2rdo = q' In odo. equation

A:

Q: 5. Consider the function f(x)=e*, calculate df/dx with finite difference using forward and central…

A: We can solve this using formula of central difference and

Q: Show detailed solution to the following using ti integration. x'dx 1. Integration by Parts J Vx4-5

A: Let's find.

Q: 1. Evaluate S x³V1+ x² dx using Integration by parts.

A:

Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2 + 3/x) dx. 1+x² I =

A:

Q: Find a general solution of each reducible second-order differ- ential equation y" = (x + y')²

A:

Q: Find a general solution of each reducible second-order differ- ential equation y" = (y')2

A: Given, The differential equation y"=(y')2 .               ................(1)

Q: The rate at which the total average of COVID cases is dx increasing at x = 10 tents and = 1 tent per…

A:

Q: Find the general solution to the DE using the method of Variation of Parameters: у" — Зу" + Зу' — у…

A: The solution is given as

Q: 7. Evaluate the integral. Vx2 – 25 dx х3

A: First we will make a trigonometric substitution of x=5*sec θ then we will solve it and integrate it.…

Q: Match the graph with the first order differential

A: In this question we will use basic concepts of calculus i.e graphing of differential equation.…

Q: Š The minimum value of n required to approximate dx by composite Simpson's Rule with an error less…

A: Given integral is ∫02e−2xdx. We have to find the minimum value of n required to approximate…

Q: 13. The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03…

A:

Q: 6) Use the successive approximations method to solve the following Volterra integral equation: (x 2

A:

Q: Device 2 is capable of detecting seismic changes up to a distance of 1.4 times that of device 1.…

A: In this we have to do the given instructions and approximate the value to the nearest 100,000 and…

Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson's 3/8 rule with (n₂ = 3) to estimate tan-¹(2).…

A: We have to estimate the given function.

Q: Only one of these calculations is correct to evaluate the definite integral Vx+1 dx Using the…

A:

Q: 2. The rate at which the total average of COVID cases is dx = 1 tent per day, given dt increasing at…

A: Given,  number of tents= 20 and average number of cases will be 5