2. Approximate (x-3) dx using 4 rectangles. It is approximatiley (If necessary, round to two decimal places. Do NOT ro

Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: The following problem is for extra practice and does not have to be submitted. 2 1 -dx using the…

A: According to question ∫0211+x3dx,       n=4

Q: Evaluate dy/dx at x = 2.5, correct to 3 significant figures, given y= (2x^2+3)/In 2x

A:

Q: Find dy dx? if y= 5cos2x-4sin 2x at x =0

A:

Q: Integrate the following using ~2 x+1 2. dx

A: ∫12x+1xx-1dx

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

A:

Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

A:

Q: (a) Determine the interval width so that the composite trapezoidal rule can be used to compute xe*dx…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: find the following intergral X^2+1/ X-1 dx

A:

Q: to determine the approximate value of v(1+x³)dx

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Q: Select the correct answer. What is the value obtained by using left endpoints with n= 4 subintervals…

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Q: Use trapezoidal with 3 level Romberg ( k=3) to evaluate 1 Пх - Пх* cos dx 4

A: The complete solutions are given below

Q: 5 dx, correct +2x²) Problem 19. Evaluate (3 to 4 decimal places

A: ∫0152x2+3dxSubstitute u=2x3→dudx=23→dx=32du=∫532(3u2+3)duSimplify:=523∫1u2+1duWe know that…

Q: Approximate 2x e 2 dx using three equal subintervals. - 1

A: To Approximate

Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

A:

Q: Given tanh-1(xy) = xy, find d²y dx2

A:

Q: Use symmetry to evaluate the followingintegrals.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: az for a – yz+ sin(cyz) = 5. dx 9. Find %3D

A:

Q: B. Use the trapezium rule with 6 ordinates to estimate fe* dx correct to two decimal places.

A:

Q: find dy dx 15 In 4+ xe) 6

A: dlnax+bdx = a.1ax+b.

Q: sin(x+y)=xy  what is dy/dx?

A:

Q: Find e dx approximately using Simpsons rule with n 10.

A:

Q: 2x dx by taking n = 4 1+ x Use trapezoidal Rule to evaluate

A: trapezoidal rule

Q: The area under the entire curve is given by 00 dx. We have 3x-3 dx = lim 3x-3 dx -2 3x lim %3D -2 x…

A: the area under the  entire curve is given by ∫1∞3x3dx

Q: FIND DY/DX OF THE FOLLOWING 6. y=sec'Inx

A:

Q: dy Find for dx 4) y= sinxtanx

A:

Q: 1. dx Evaluate 0, et +e-*

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Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: 1 dx (25 – x2)3/2 - Show My Work (Required) ?

A:

Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places…

A:

Q: Use the Trapezoidal Rule with n = 6 to ex approximate dx | 1 х Use the Simpson's Rule with n = 6 to…

A:

Q: 1. Differentiate the following: а. у %— y = x²e2x, find dy/dx

A: Differentiate the following

Q: Find dy/dx for following functions. 1) y = csc-(e2inx?) + sin-1(2lnv3x)

A:

Q: Given y=−3cosx, what is dy/dx?

A: y=-3cosx

Q: 1 Evaluate dx by using Trapezoidal rule. Hence obtain 1 + x2 he approximate value of .

A: I am attaching image so that you understand each and every step.

Q: 2x dx by taking n = 4. 1+x Use trapezoidal Rule to evaluate

A: on solving this we get

Q: Solve the following Exact DE using Method of Grouping. 3) () dx + () dy = 0 X-X y

A: Given:          2x-1ydx+x-x2y2dy=0     This is in the form of   Mx,ydx+Nx,ydy=0    where Mx,y=2x-1y…

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

A:

Q: Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x)…

A:

Q: The approximate value of dx by using Simpson's rule is 0.3480, then the error in the approximation…

A: Given Approximate value of the integral by Simpson's rule(Vs) = 0.3480 Now we will find the actual…

Q: 4-3x dy dx X,

A: its a multiple integral based question.so 1st we integrate with respect to y and then with respect…

Q: Use the trapezoidal rule withn= 4 to approximate cos(x) dx Keep at least 2 decimal places accuracy…

A:

Q: Approximate S“ In x dx using three rectangles of equal length and left end points. Is your estimate…

A: The given integral ∫1e2ln x dx, three rectangles and left end points.

Q: Use the Trapezoidal Rule with n = 4 to approximate the value of: +1)dx.

A: Given,  ∫12x3+1dx, n=4

Q: 5) Approximate -dx 1 +: Using the Trapezoidal rule and Simpson's rule with h=1. Find an error in…

A: We have to use both numerical methods for 4 subintervals as h=1 and (b-a)=4.

Q: The approximate value of| dx by using Simpson's rule is 0.3639, then the error in the approximation…

A: Approximate value of ∫161x4dx by using Simpson's rule is 0.3639 To find the error in the…