2. Find a) ³ dx b) xdx. Hence, find whether the following integrals exist and, if they do, find their value. d) dx.

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

Q: To find the arclength of y = 2x2 – 1 from æ What is the value of the integral? O to x = 3,

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Q: Calculate this integral a Sat-x? 3/2 x²+y²)¯ dy dx -a

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Q: Evaluate the integral using the given substitution. Jx cos (6x?) dx, u=6x? x2 O A. sin (6x?) +C 2 1…

A: As per our guidelines we need to solve only one question.please repost the remaining questions as…

Q: 4. Evaluate the following integral using three-point Gauss-Legendre quadrature: 3.5 dx Vx2 - 4 3.

A: We will use the three-point Gauss-Legendre quadrature. First we convert the given integral…

Q: Evaluate the integrals in Exercises  by making a substitution(possibly trigonometric) and then…

A: since you have posted multiple questions so I'll solve first one for you , for rest question's…

Q: Use the substitution formula to evaluate the integral. S'ia dx (Hint: simplify first) 1 2 11 22

A: Solve the following

Q: Let a, b> 0, then the integral x2a +1(1-x²)bdx, after changing variables y = 1– x will be expressed…

A: Given the integral I = ∫01x2a+11-x2 b dx To changing variables y = 1-x2 will be express

Q: S)Use the Fundamental Theorem of Calculus to decide if the definite integral exists and either…

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Q: a) Evaluate the integrals using appropriate substitutions. dx Sino i)S i) f de Cos? 8+1 1+16x2

A: as per our guidelines I am solving only first question with both parts a(i) ∫dx1+16x2ii ∫sinθcos2θdθ

Q: eln (R/c) secx - sec?x)" sec(34 – x) "du?? dx to be integrable using the formula What should be the…

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Q: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…

A: Using green theorem to evaluate the following integral.

Q: Use the calculus of residues to evaluate the following integral 27 1 de. 1+8 cos? 0

A: Given integral is ∫02π11+8cos2θdθ

Q: Evaluate the integral by using the substitution u = 1 + e*. 1 – e* %3D dx 1+ e*

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Q: let b be a constant. use definition to find  (integral 0 to b)(x+1)^2 dx.

A: Given: The expression of integral as ∫0bx+12dx, where b is a constant, To evaluate: The value of…

Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h=; , to approximate the integrale-2x²…

A: Note:- As per our guidelines, we can answer the first part only as both are different and first part…

Q: tan(x)dx, Ind: u = cos(z)

A: We have to calculate the given integral: ∫tan x dx We know the identity, tan x=sin xcos x Therefore,…

Q: By making an appropriate substitution, which of the following integrals is equal to | tan (x)…

A: make a substitution for choosing the integral.

Q: Use quadrature formula [f(x) dx = c f(0)+c₁ f(x) to approximate the value of the integral [x² In x…

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Q: C for the con

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Q: Use the fact that cos(z) = R(eiz) = (eiz + e-iz)/2 to find the integral of (e3xcos(4x))dx.

A: Here the given integral in not in the complex form so we calculate the integral as it is given in…

Q: Evaluate the integral of (3x + 9y) dx dy, use the inner limits from 0 to y and outer limits from 0…

A: Given: The double integral ∫∫3x2+9y2dxdy, here the inner limits varies from 0 to y and outer limits…

Q: Evaluate the integral. 'Tt/2 7 cot (x) dx T/4

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Q: In Exercise, evaluate the given integral.∫(xcosx+xsinx)dx.

A: Given: ∫x cos x + x sin x dx To evaluate: The given integral.

Q: Use the substitution formula to evaluate the integral. dx 1. 22 11 11 O00

A: Solving the problem by substitute method.

Q: Evaluate the integral. 3x/4 csc e cot e de a/4

A: Given that integration of (π/4 to 3π/4) csc(theta)cot(theta). We know that csc(theta) =…

Q: Set up, but do not evaluate, an integral for the length of the curve. y = x - 3 In(x), 1< x < 4 4 dx

A: The given curve y=x-3 ln(x), 1≤x≤4

Q: Calculate the iterated integral o L? 5x cos y dydx

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Q: (2 + x /T)dx

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Q: 1- Assume that x, y € R and z = x + iy € C .Calculate the following integrals using the given…

A: a) Given ∫0∞lnx1+x2dx ∫0∞lnx1+x2dx=12∫-∞∞lnx x-ix+idx=122πi Resi=πiln i2i=π2ln i=π2ln1+π2 i=π20+π2…

Q: , evaluate the given double integral. I sinxcos(y – n)dxdy 10.

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Q: The length of the curve y=In sec x from x=0 to x=b, where 0 < b <, may be expressed by which of the…

A: Given length of the curve y = ln secx.Below find the solution in the image.

Q: Evaluate the integral. NÓTE: Enter the exact answer. xy" dy dx

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the iterated integral. •x5 V 64 – x6 dy dx /o Jo

A: The given integral is:∫02∫0x564-x6dydxWe need to evaluate the integral.

Q: and evaluate the Sketeh, integral reverse Jy dx

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Q: 11. The integral of nunex dx is bln]sec(In(2x)")|. What is b? A. 2 B. 2 C. 4 D.

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Q: 1 dz c+x2 c)

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Q: Evaluate the integral cot2x dx J Tcot?x – 15

A: We will evaluate the given integral as shown below

Q: To evaluate the integral Vx2 + 4x + 5 dx using a trigonometric substitution, use the substitution…

A: As we know that 1+tan2x=sec2x

Q: x2 dx 3. (бх2—49)"/2 49 [V36x3-9x IVox + v6x2 –9 + In + C I 12v6 49 7

A: In this question we will use basic of calculus i.e concept of integration. We will simply use…

Q: The resulting integral of S dx is In + e Tan"1+ C where a, b, d, and e are integgrs. x+x²+4x+4 What…

A: Differentiate the result of the integral:…

Q: Evaluate the followaing integrals Li (1– 2sin?(x).sin(4x) dx) |

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Q: Evaluate the integral. e sec²(8x) dx %3D +C

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Q: Use the Residue Theorem to evaluate the a? integral dx + x2 where a>0

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Q: 4. Evaluate the following integral using three-point Gauss-Legendre quadrature: 3.5 dx Vx2 – 4 3.

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Q: Set up, but do not evaluate, an integral for the length of the curve. y = x – 9 In(x), 1sxs 4 dx

A: The integral for the length of the curve is  L=∫ab1+dydx2dx

Q: Evaluate the following integral: J Sec?x -dx V1-tan2X

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Q: Compute the integral | x"dx, with a=1, b=7, and N=5. Answer to three decimals.

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Q: Find the value of P which the integral convesg'es,absolubely Conditionally Sin Vz) dx .P

A: