) Evaluate the integrals of the following; i) ,( + cos x)dr 1+cos 2t dt ii) 2 iii) [(3x +2)(3x? +4x)* dx, u=3x² +4x

Q: The value of the binary integral is e-xy dxdy . (where a, b are positive real constants) are

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Q: a) Evaluate the Rollowing integrals 2) sinrde 3)

A: Answer and explanation is given below According to guidelines,i will provide answers of first three…

Q: 8. Find the general indefinite integral (x³ -2² + x)dr; b) / (2" +-)dr, x > 0; c) (sin(3t) +…

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Q: 7. Evaluate the integral. J CoS X dx 0 1+sin2x

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Q: Calculate the iterated integral A 67 5x cos y dydx. 1 2n 5

A: Explanation of the answer is as follows

Q: Evaluate the integral. S 20x cos x dx Select one: O A.80 sin. 1 40x cos + C O B.20 sin n1)x+ 40x cos…

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Q: Find the indefinite integral: 10sin 3x - 15 cos 2x + 6 e5x + C O 90sin 3x -60 cos 2x + 150 e5x + C…

A: 30∫cos3x+sin2x+e5xdx=30· ∫cos3xdx+∫sin2xdx+∫ e5xdx=30·…

Q: Evaluate the integrals: 1₁ = - S using Second-order Gauss quadrature. O I₁ = 3.1416 12 = 1.5708 1₁ =…

A: Second - order Gauss quadrature formula:…

Q: 2. Use Cauchy's Integral formula, Evalnate the following. • I= 6 Sin4Z :(Z-4)3 IZ1= 3 I = . tanttz…

A: Given

Q: Find the indefinite integral: 30 [cos 3x + sin 2x + e5x]dx 10sin 3x -20 cos 2x +6 e5x + C O 90sin 3x…

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Q: 4. .2 + 2x) cos(2x) dx

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Q: 5) Evaluate the integral.cusc c for the constan6 of integrafion) 2(ean cx) +6an cx>) dx

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Q: .3 S cos³xVsinx dx

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Q: х cos 4x dx; и 3D х, dv cos 4x dx =

A: Given that  u = x ;  dv = cos 4x dx and we have to integrate by parts the given integral that is ∫x…

Q: 2) Evaluate the integral S inx dr 2.

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Q: 4 – dt 2 cos 4t 1.

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Q: Find the indefinite integral: O 10sin 3x - 20 cos 2x +6 e5x + C 90sin 3x 60 cos 2x + 150 e5x + C…

A: The objective is to find the indefinite integral.

Q: Evaluate the integral: f sin 7x cos 2x dx. A) sin 5x + sin 9x + c. 2 B) cos 5x +co cos 9x + c. 10 C)…

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Q: 1. Evaluate the followmg integrals 5x2-14x+6 x3-3x2 a) xp b) (cos-esmode

A: We have to find the given indefinite integration

Q: Evaluate the integrals

A: We have to evaluate the integral ∫0π21-cos2θdθ We know that, 1-cos2θ=2sin2θ Therefore,…

Q: Evaluate the integral. Sex. cos 3x dx e2x [ sin 3x + cos 3x] + C O e2x [3 sin 3x + 2 cos 3x] + C 13…

A: Given: ∫e2xcos3x dxe

Q: Evaluate the integrals

A: Solution -  Given Integral equation - y = ∫π201+cos2t2dty =12∫π20dt + 12∫π20cos2t dtUsing…

Q: Compute this integral ∫ (xsin^2(x)cosx) dx

A: We use integration by parts

Q: 215 5. (a) Transform the real integral Pz dr into a complex inte- gral clearly specifying the…

A: We transform given integral into complex integral.

Q: Find the indefinite integral. 4x2+2x-1 d.x none of these Omz + 1| -31m|z미-글+C o+ Inz* + =*|+C In a+1…

A: Given: I=∫4x2+2x-1x3+x2dx   We know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And…

Q: Evaluate the integral. 3x cos 2x dx O e3x [2 sin 2x - 3 cos 2x] + C 13 O 1 [2 e3x sin 2x + 3 cos 2x]…

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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: Evaluate the integrals ∫et cos (3et - 2) dt

A: We have to evaluate the integral: ∫et cos3et-2dt In this case we should use substitution method…

Q: Evaluate the integrals ∫8 cos4 2px dx

A: To evaluate: ∫8cos42πxdx Let t=42πx dtdx=42ππdt42π=dx Putting the values, we get…

Q: 1- Find the integral of: 2 cot - de 3 7/2 A- B- dr Vr

A: (A) Given integration is : ∫π2π2cotθ3dθ Use property of integration ∫cotaxdx=logsinaxa+c

Q: 1. Use the Table of Integrals in the back of your textbook to evaluate ∫11dx/x^2√16x^2+36 a.Perform…

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Q: cos'xsin*xdx IN

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Q: Use the form of the definition of the integral given in Theorem 4 in section 5.2 to evaluate the…

A: First integrate the function x2+7 with respect to x using the power rule of differentiation.

Q: Evaluate the integral. Select the correct answer. 1 15 cos ²6 x - = cos 6x + C cos³6 6x- 18 O…

A: Given :∫sin36xdx

Q: Can i get help step by step with this problem?

A: Given:

Q: Evaluate the integral of cos^2 ydy

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: You found that the reduction formula of a certain integral is In = a" sin 2x + nx"-1 cos 2x – n (n –…

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Q: 7. | (x² + + 2x) cos x dx

A: Apply the integration by parts in the given integral. Let  u=(x2+2x) ; dv=cosxdxThen,du=2x+2dx ;…

Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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Q: Find the definite integral of ³ Option 1: 4 Option 2: Option 3: Option 4: Option 1 Option 2 Option 3…

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Q: You found that the reduction formula of a certain integral is In = 180 (13x" sin (13x) + næ"-1 cos…

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Q: 9. In evaluating the improper integral dx , which of the following is true? (1-3x)2

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Q: (integral of -4 to 4) of 5*cos(3t)(delta(t))dt

A: Here,

Q: Prove the following integral sen2x а) dx cos4x + sen4x arctg(2 sen?x – 1) + C ans.

A: Note: senx is written as sinx.   We know that: a2+b2=a+b2-2ab2sinxcosx=sin2x∫11+t2=arctg(t)+C

Q: 3 In 3x Evaluate the defınite integral : J 6x2

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Q: Evaluate the following integral. cos x dx -6x 1 sin 2x dx 2 - 6n O C. dx + cos 2x dx OD. dx + - 6x 6…

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Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 b. dz a. √21-23 = dz · Soz (²-2) 4…

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Q: 5, set up the appropriate iterated integrals in rios for I f dV on the indicated domains.

A: Step:-1 Given that  The equation of tetrahedron is z = 4 -2x -y⇒2x + y+z =4 ---(1) so, bounds or…

Q: Evaluate the double integral : 9 dy dx 36 – 12 - 12 -36

A: