Watch the video on the integral of 1/(9-x^2) e before answering t What substitution could you make to compute da V3-a2 O x = 3 sin 0 O x = 3 cos 0 O x = V3 tan 0 Or = V3 cos 0

Q: Express lim Σ n → ∞i=1 3 n ( n 3i + COS 9/² 2 as a definite integral

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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: Evaluate the definite integral. π/2 1- cos(2x) dx

A: Answer:-(1) Given the integral,     ∫sin2x cos22x dx=∫44*sin2x cos22x dx…

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: Evaluate the integral: integral from 0 to Pi/2 of cos^3(x)*sin^(2/3)(x)dx

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Q: Use integration by parts to show that, for n > 2, 1 cos a sin"-1 n 1 sin"-2 xdx. n - sin" xdx = x +…

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Q: Evaluate the integral.  integral  sec 3 x  tan  4 x  dx

A: Given

Q: 5tan 2x -dx sin²2x-1 8.

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

Q: Use integration by parts to evaluate the integral: sin(In(9x))dx 1 x(sin (In)(9æ))– cos(In (9x)) + C…

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Q: Evaluate the iterated integral. 1-sin 0 r cos 0 dr d0 1-sin 0 cos 0 dr d0 =

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Q: •3 sin (7|3 – 2x) dx

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Q: 1 (7 – x²) sin nxdx An 2(-1)"+1 n3 II

A: Integration by parts  ∫U·Vdx =U·∫V dx-∫dUdx∫V dxdx Where U and V are the function of x . Also,…

Q: Evaluate the integrals

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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: Which integral should be used to find L {sin 3t}? a. sin 3t dt d. o -st sin 3t dt e b. Se-st sin 3t…

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Q: Evaluate the definite integral 3 5/3 dx 1

A: Evaluate the definite integral

Q: sin 40 do 9 + cos 40 Evaluate the integral ; using the substitution u = 9+ cos 40. sin 40 do 9+ cos…

A: ∫sin4θ9+cos4θ dθ

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: Find the indefinite integral ∫tan3 2t sec3 2t dt

A: We have to evaluate ∫tan32t sec32tdt Given integral can be written as: I=∫tan22tsec22t sec2ttan2t…

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: What is the integral of sin^4(x)cos^3(x)

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Q: What is the value of definite integral ∫ (top of ∫ Is 1, bottom is 0) -6x^3(3x^4-2)^5 dx. Enter the…

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Q: Ssin( /3x)cos(-2r)dx

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Q: The definite integral sin24x cos2x dx is equivalent to x/2 (A -sin²0 cos²0 d0 2 x/2 В 2sin20 cos40…

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Q: Transform the integral 7 n do d0 by the substitution r = sin o cos 0, y = sin ø sin 0 and then sin 6…

A: The formula for change of variables is given by ∬Rf(x ,y)dxdy=∬Sf[x(u,v),y(u,v)] ∂(x,y)∂(u,v) dudv…

Q: a) Evaluate the integrals using appropriate substitutions. Sine ii) S de Cos0+1

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Q: Find the indefinite integral. S-x² + sin x – 3* dx | In |x| – - 3* + C COS X - 3 In 3

A: detailed solution is given below

Q: Evaluate the integrals ∫sin 2θ - cos 2θ/(sin 2θ + cos 2θ)3 dθ

A: We have to evaluate the integrals: ∫sin2θ-cos2θsin2θ+cos2θ3dθ This integration will be solve d by…

Q: 12 cos6x. sin³ xdxCalculate "/2 3 the integral

A: It is integral problem.

Q: Evaluate the indefinite integral: S 9x“ cos (x³ + 6) dæ COS

A: Given,  ∫9x4cosx5+6dx  We have to evaluate the integral using substitution.

Q: TC O. Evaluate the definite integral : 6 sin(8t) dt Round your answer to 3 decimal places.

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Q: Why is the integral here not pi/48? Is there something wrong with my process before evaluation of…

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Q: (A very cute proof ) I want you to show using integration by parts that sin(mx) sin(nx) dx = 0 if m…

A: To show: ∫0πsin(mx) sin(nx) dx = 0 We know that, Integration by parts ∫u dv = uv - ∫v du Suppose, u…

Q: Evaluate the integral cos3 x + sin? х+1 dx cos² x (sin² x + 1)

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Q: What substitution should be used to solve the integral O sinu=3x/2 O sec u =2x/3 O sec u =3x/2 O tan…

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Q: Evaluate the definite integral. 13 dx 3 (1 + 2x)2

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Q: The undefined integral of the function [1+ cos x} power -1 is *

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Q: Evaluate the definite integral: 2 1 de sin 0 + cos 0 +1

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Q: sin° (2æ) cos(2æ)dæ

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Q: Match the integral expression on the left to an equal expression on the right. Prompts Submitted…

A: 1. =∫2sin(3x) sin(4x) 2 dx=∫12-cos3x+4x+cos(3x-4x) dx=∫12-cos7x+cosx dx=∫12[cos(x)-cos(7x)] dx

Q: 7. Find the indefinite integral. (a) / 3 cos(") dz /32c0 31 dr

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Q: solve both without using the table of integrals. Q1) integral of cos4xdx   Q2) integral of tan5xdx

A: according to our guidelines we’ll answer the first question since the exact one wasn’t specified.…

Q: | sin(ax) cos(ax) dx

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Q: Match the integral expression on the left to an equal expression on the right. cos(7x))dx + cos(…

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Q: Match the integral expression on the left to an equal expression on the right. cos(7x))dx + cos…

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Q: Evaluate the definite integral. 1/5 5 dx V1- 25x2

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Q: 2 sin6 x cos⁹ x dx 0

A: See the details solution in below

Q: Evaluate the integral: 30dx / (1-cos(5x)) The solution to the integral is -6(Cot(5x) + Csc(5x)) + C…

A: Multiply by (1+cos(5x)) in numerator and denominator.

Q: Use integration by parts to evaluate the integral: sin( – 8r)dr - 05 e-r(sin(-8r) - 8 cos (-8r)) + C

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