2. Use Cauchy's Integral formula, Evaluate the following sin42 IZ1= 3. (Z-4)3

Q: Evaluate the indefinite integral; f Vtan 3x sec2 3x dx OA)-(2(tan [3x)^(3/2) ] /9 + C OB) I DON'T…

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Q: Evaluate the integral. 17) S sin (3x - 2) dx

A: From the given problem:   I=∫ sin3x-2dx..(1)   Let,   u=3x-2   Now differentiate with respect to x:…

Q: 3 sin 3 ycos ydy

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Q: evaluate the indefinite integral

A: The given integral is

Q: •2 dx

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Q: 3 Which of the following is equal to sec ² x tan³x dx to obtain the correct indef inite integral?

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Q: 3. Use the Fundamental Theorem of Calculus to evaluate the definite integral 16 x Vx dx 4

A: Given: ∫416xxdx Simplifing the given integral∫416xxdx=∫416x(x12)dx                 =∫416x1+12dx…

Q: Evaluate the integration 2.5 o cos(x) with h=0.5 by using 3/8 Simpson Rule. Write your answer in 4…

A: The Simpson's 3/8 rule states,∫ydx=3h8y0+2y3+y6+ . . . + yn-3+3y1+y2+y4+y5+ . . . +yn-2+yn-1+ynWe…

Q: 9. Find the integral, using u substituti x-(1-3x²)*dx a.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 14. Verify that f cotx dx = In(sin x) +C. (Do not try to solve the integral from scratch.) %3D

A: Given: verify that ∫cotxdx=lnsinx+c For verifying given integral, we integrate given integral

Q: 5tan 2x -dx sin²2x-1 8.

A: Put tan2x=t and using integration of ax dx =ax /loga

Q: Calculate the integral of y = 11 cos (8x) from 0 to Answer = Number Leave your answer in exact form…

A: on solving this we get the

Q: What substitutions are made to evaluate integrals of sin mx sin nx, sin mx cos nx, and cos mx cos…

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Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

Q: 5. Evaluate the indefinite integral. S cososin'oc (1) (3x - 2)20 dr (2) (3) S etanr sec?rdr

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Q: Use the results of Section 5.2 to compute the following definite integral: 3x² dx

A: We need to evaluate the following integral ∫-453x2dx Formula Used : ∫abxndx = 1n+1bn+1-1n+1an+1

Q: Evaluate the integrals. ∫sin 2x/(1 + cos2 x)dx(Hint: sin 2x = 2 sin x cos x.)

A: We have to evaluate ∫sin2x1+cos2xdx We know that sin2x=2sinxcosx So, the given integral can be…

Q: Use the substitution æ = 2 tan(0) to evaluate the indefinite integral 4dx V + 4

A: NOTE: Refresh your page if you can't see any equations. . ...............(1) substitute…

Q: Evaluate the integral: 2 So sin(4t - u) du dt

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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: Compute the approximation  of the integral -4 to 4 e^(-x^2) using right endpoints with 4 rectangles;…

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Q: Evaluate the indefinite integral: (8e" + 5 sec? u) du =| + C.

A: We use integration of eu=eu and integration of sec2u= tanu .

Q: 5) Evaluate the integrals using appropriate substitutions a) sec 2x tan 2x dx b) 2x+1

A: Given that, a) ∫sec32x tan 2x dx b) ∫x2x+1dx For evaluating those indefinite integrals,  we need to…

Q: 2. Use Cauchy's Integral formula, Evaluate the following • I= sin4z ,IZl= 3

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

Q: Evaluate the definite integral. rIn 3 8e-X cosh x dx

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Q: Identify an analytic anomaly why numerical integration formulas will fail for J_11-x² sin(ax) dx.…

A: Given integral is∫-11sinπx1-x2dx

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: set up an integral ....bounds x=3pi/4 x=-pi/4 y=-sinx and y=-cosx

A: GRAPH

Q: Evaluate the indefinite integral.   ∫ Sec3t  tan 3 t dt

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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 integral.

A: Consider the following integral:…

Q: evaluate the integral (Usec. af nitegratun) for the constant बदेशव 1ehan) 5x cos (8x) dx

A: Given

Q: Use the results of Section 5.2 to compute the following definite integral: 4x2 dx %3D

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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 indefinite integral.

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Q: Evaluate the indefinite integral: (3e" + 6 sec? u) du: |+ C.

A: As per guide line we have

Q: 4. Prove using the results concerning iterated integrals that In 5 dx = 4 sin? x

A: Given:-                 To prove the result concerning iterated integrals that…

Q: 20. Verify by differentiation that finx dx = x(In x-1) + C, then use appropriate changes of…

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Q: Compute the approximation  of the integral -4 to 4 e^(-x^2) using mid points with 4 rectangles, you…

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Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

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Q: Use Cauchy's Residue Theorem to compute the improper integral (x + 3) sin(x) dx (x2 + 1)(x² + 4)2 00…

A: Given that ∫-∞∞x+3 sinxx2+1x2+42dx Using Cauchy residue theorem, we can written it as ∫-∞∞z+3…

Q: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

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Q: To evaluate the integral dz, we use Select one: Substitution with z = 2 sin 0, where 2 O…

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Q: 1. Use the table of integrals to integrate the followin a) S sin ) s in () dt

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Q: In x dx

A: Given: ∫lnxx2dx Integrate the given integral using the integration by parts formula.

Q: 3. Evaluate integral by using a basic substitution: S x² sin xdx

A: Given: ∫x2sinxdx To evaluate: The given integral.

Q: Solve the integral by two grid in the y-direction and four grid in the x-direction with Trapezoidal…

A: The given integral is: ∫45∫23xcosydydx Here  x0=4, x1=5y0=2, y1=3fx,y=xcosy By 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: sec² (1+ /7) dr. 6) Use the substitution u = 1+Va to evaluate the indefinite integral|

A: