L*(; 12 2ху To compute /x²+y²+3 ) axay you do the u substitution: u = (Notice that this is a substitution for the inside integral in x) du = •12 2ху dxdy =

Q: Q.3 Find the double integral for Sl. x2 dydx, where R between y = -4/x y = -x and x = -4

A: Ti evaluate the given double integral  first we draw  the region

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Q: Evaluate the integral. 16 In(y) dy Vy

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Q: dx Evaluate the integral V1 + 9x² 1) Which substitution will change the integral into one of the…

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Q: 2- Evaluate the integrals in Exercises 7- 8- 9- In 9 Son 24/2 In 4 S dr [ 21 e ² dt ex/2 dx

A: To evaluate the given integrals.

Q: I.Evaluate the ff. iterated integrals. rd/2 ptan y sec y 1. x'cos' ydxdy

A: Please see the answer below.

Q: Can you help step by step please?

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Q: Evaluate the integral dx (5ӕ + 10)2 by making the appropriate substitution: u = dx (5x + 10)? II

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Q: Evaluate the improper integral 2). L, xe-** dx

A: To solve the improper integral

Q: dx Evaluate the improper integral if it exists 2.10 6.2 0 The improper integral diverges 30 .40

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Q: Use a substitution of the form u = ax +b to evaluate the indefinite integral belov 7x+1 dx 7x+1 dx%=

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Q: 14 Find the integrals using integration by parts. b. JF In /rdx In a. fx(x + 4)°dx c. fr'e"dx d.…

A: Just multiply by 1and go ahead.

Q: Evaluate the double integral: (y 8r) dr dy

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Q: Evaluate the integral *(* – 10)"dz 6 by making the substitution u = 1 z° – 10- +C

A: ∫un du = un+1n+1+C ; where 'C' is an integration constant.

Q: dx Evaluate the improper integral if it exists The improper integral diverges 10 6.20 8.4 O

A: Given that  The improper integral is

Q: Q5. 4 Evaluate the improper integral J, - dx 1 x(Inx)7

A: Given ∫1e4xln(x)substitute u=ln(x) => dudx=1x => dx = x. du=4∫1e1uduNow solving 1uduApply…

Q: dz 2ydy In if we let y=z + 4, then the new integral becomes Vz+4 -2 у-2

A: Follow the procedure given below.

Q: Evaluate the integral 20 | by making the appropriate substitution: u = 5 – 2 (2³ – 2)® dx %3D -

A: Evaluate the integrals

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

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Q: 00 1 (b) Calculate the improper integral dx , or show that it (x² + 25)3/2 -00 diverges . Show your…

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Q: Q5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² 1 the polor…

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Q: g integrals. tion. (Use c1 and c2 for c, and c2).

A: Given, the nonhomogeneous differential equation :           y'' + 3y' + 2y = 2e-t.

Q: Evaluate the integral 4 (y 2)(2y1) dy Jo

A: To evaluate,

Q: 2/in Jin3 e dxdy a) By using the change of order evaluate the integral y/2

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Q: Evaluate the improper integral if it exists 1 dx: .1 2/2 .2 .3 The improper integral diverges .4 2.

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Q: (d) Prove that 1-cos 2x dx is divergent. Hint: Split the expression inside the integral into two…

A: Integral is converges or divergence

Q: 3 1 L₁ dz -3 (x+2) ³0 Compute the integral:

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Q: (유) 6. dy dr Evaluate the double integral:

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Q: Evaluate the Integral by changung the order of Integration in an appropriáte way. 4 3 5 Cos (x?) dx…

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Q: To find the arclength of y = 2x – 3 from = 0 to x = 4, which is the correct integral? OL = V1+ 4x²dx…

A: I have appended the formula used in the solution part.

Q: 14 Find the integrals using integration by parts. -2 b. JVF In Vxdx a.

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Q: Evaluate the improper integral dx (5 – x)³ K MANUSIA KERANA T

A: Recall: Improper Integral:      If f(x) is continuous on the interval [a,b) and not continuous at…

Q: 15 Evaluate the improper integral J. (x- dx

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: If -2 f(2)dz = [ f(2)dz + what are the bounds of integration for the first integral? and b =

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Q: Q2/Evaluated the integrals v2 1- f– (1-v2 )2

A: The integration of v2/(1-v2)5/2.

Q: Evaluate the integral. 2 - 121 y - 121 2 -dy, y> 11 dy=

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Q: evaluate integral of Ś t^2 ln(t) dt

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Q: 3 3y Evaluate the iterated integral ry de dy.

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Q: dz ins- , if we let y=Vz+4, then the new integral becomes z+4 -2 у-2 True B False

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Q: | 2°+Idal Vx² +1 dxl

A: The given integral is- ∫x3x2+1dx Let x2+1=u Differentiate w.r.t. x to both sides- 2x=dudxdu2=xdx…

Q: 1. Evaluate the integral using Integration by Parts. (a). S In(Inx) dx.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 1+1 dz is 1+ z6 By comparison test, the improper integral

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Q: evaluate the integral by mahing (use c for the' constant of htegration) Mtegration) the qiven…

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Q: Compute the given improper integral. Enter the exact value of the answ 13 1 dx x² – 25

A: Here we have to find the exact value of ∫5131x2-25dx=?

Q: what is the integral of z 3^z dz

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Q: 5. (a) ( If ryz² + x²yz + ry²z = e*v², compute . (b) Let f(r,y) be some function. Set up the…

A: (a) The equation given in the question is: We need to evaluate  This represents the derivative of…

Q: /2 etan y sec y х cos" ydxdy

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Q: Evaluate the improper integral if it exists dxp: 2.10 0.20 The improper integral diverges 30 2/2 40

A: Option (3) is correct. Integral diverges.

Q: Evaluate the improper integral if it exists 2.1O 1.2 O The improper integral diverges 3 0 6.4 0

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Q: x+y xydx dz dy Jo

A: