Q2\ Find the limits of the following integral ym Inx 2 4 cos 20

Q: Evaluate the integral: integral fom 0 to pi/2 sin^2 x cos^2 xdx

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Q: Evaluate the integral. 3 1 3y2 cos xy dy dx x/3 5(1 - cos 3) 3(1 - cos 3) cos 3 - 1 (1 - cos 3)

A: Formulae used: ddxxn=nxn-1∫cos(ax)dx=sin(ax)a+C∫sin(x)dx=-cos(x)+Csin(0)=0cos(0)=1

Q: Evaluate the integral. 6. 9 In(y). dy Vy J4

A: Given,             ∫49lnyydy

Q: Evaluate the integral. 4 f(x) dx where f(x) = if -3 Sx 0 0 <x < 3 6 - x2 if

A: we have to find the following integral

Q: x cos TX dxr Jo

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Q: 2. Identify which of the following integrals are improper: 1 1 dx 1 fin(x)dx 1 X +3 1 fe* dr -dp- 3

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Q: Find the integral J dx using the following methods: х2 — 9 -

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Q: Q5. Evaluate the improper integral dx x(Inx)7

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Q: Evaluate the integral. (x6 + 4y³) dy

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Q: 4 1 : Evaluate the following improper integral by using proper limit notations: dx. (4 – x)2/3

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Evaluate the integrals ∫4/y2 dy

A: we have to evaluate the integral ∫4y2dy let the given integral be I. therefore,…

Q: Evaluate the integrals below: 1 2y .dx cos3x а) .dx, b) 0. lelsin3x – 1)

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

Q: 1. Rewrite the following improper integrals as a limit and then evalute them, or state that they…

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Q: Q2:A/ Evaluate the integrals sec (1 + ex) tan (1 + e'/x) dx

A: Integral

Q: Show using residues that   the integral from 0 to infinity of dx/(1+x^6) equals (2pi)/3

A: We have to show that ∫0∞dx1+x6=2π3 by using residue theorem. Now, ∫Cdz1+z6=∫−RRdx1+x6+∫γdz1+z6 Now,…

Q: Evaluate the integral 3 2x cos(xy)dydx 2

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Q: The particular integral of (D2 + 1)y = cosx is -zcosz 2 -zsinz 2 ICOSI zsinz 2 O None of the choices

A: Find particular integral (P .I)

Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: Identify which among the numbers are odd-numbered integrals. 1. S21 cos 7x dx 2. S csc* dx 14. S dy…

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Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

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Q: Suppose Fas satisfies f'cx) = fex). Prove that 3fx)sin(3x) + f'cx)cos (3x) Sfewcos(3x) dx = %3D 10

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Q: Consider the following BVP: - 2u 1 1sxs2 dx Using boundary condition u(1)-u(2)-0.

A: Sincei have attempted similar problems, let me solve the given problem step by step....

Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

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Q: Jy cosy smy dy 3

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Q: Evaluate the improper integral. ∞ ∫dx/((x^2) − 1) 2

A: Given improper Integral

Q: S dy V1+9y2 3.

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Q: Evaluate the integral.

A: We have to evaluate the integral: ∫x3xx2+3y2dy Here we have to integrate with respect to y so x2…

Q: What is the integral that represents the length of the curve from x 2 to x = 4. Select one: 4 ○ ₂²(1…

A: y = x4/4  length of curve formula  = ∫a b1+(dy/dx)2 here limit given from 2 to 4  a = 2  b = 4…

Q: Find the integral of f(x³ + 1) Inx dx

A: Given :∫x3+1lnx dx

Q: Evaluate the integrals: 1. ftan5 x dx 2. f sin 2x cos 3x dx

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 1 uate the improper integral dx. x(In x)3

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Q: 25 3. In r If the triple integral fo So So (xe") dydr dz Find the upper limit value E.

A: We have to find the value of E.

Q: or show that it is divergent Evaluate the integral dx 10

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Q: Evaluate the integral. (x8 + 6y5) dy

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Q: Evaluate the integral. [4 f(x) = | 16 – x² if 0 < x < 4 if -4 sxs 0 f(x) dx where

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Q: Evaluate the integrals in 1 1. Vx(1 + x) sin x sec x dx

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Q: Evaluate the integral. dy y4 – 16

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Q: Evaluate the integral. 7 - x2 | x5y dy

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Q: /2 etan y sec y х cos" ydxdy

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Q: 5 Only one of these calculations is correct to evaluate the definite integral x² In(x) dx 1 Using…

A: First we have to find h and it's corresponding formula.

Q: Q2: Evaluate the integral fx In x dx using by parts formula

A: Note:- As per our guidelines, We can answer the first question since the exact one wasn’t specified.…

Q: Evaluate the integrals ∫cos3 4x dx

A: ∫cos34x dx

Q: Express the limit as a definite integral on the given interval. „m. 2 (3(x;)° – 6x;*]Ax, [2, 6] i =…

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Q: Express the limit as a definite integral on the giv cos Xi Ax, [3x, 4x] lim Xi i = 1 4л dx

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Q: Evaluate the integral. 10 r FIL √16 22 1 (x² + y²) 1/2 dy dx dz =

A: To evaluate the integral ∫04∫-44∫-16-x216-x21(x2+y2)12dydxdz

Q: a) Compute these two integrals shown below using one application of trapezoidal rule and Simpson's…

A: Given that ∫23x dx ∫-66x2cosx dx we have to calculate given integral using  trapezoidal rule.

Q: Evaluate the integrals ∫8 sin4 y cos2 y dy

A: the given integral is: ∫8 sin4y cos2y dy we have to evaluate the given integral.   let the given…

Q: Find the Deriv ative S(x) = 4x In (1x+ t6x)

A: Use product rule to differentiate it.

Q: Evaluate the integral J 1 dx 9+x2

A: Given,             ∫19+x2dx