Is the function 3Sin26x a special function of the operator d? /dx? ?

Q: 7. S(2 + tanx)²dx

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Q: Sketch a graph of y = 8 on [- 5, 4] and use geometry to find the exact value of int -5 ^ 4 8 dx.

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Q: Evaluate in terms of beta function: (1 – +) dx. - O-8(금, 금) O-8(를, 승) O B)

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Q: Evaluate the qwen Detinite Integra ax(7-x²)* dx 2X

A: From the given integration: I=∫-3-22x7-x23dx.....(1) Using the substitution method to calculate the…

Q: Show that the functions have exactly one zero inthe given interval. r(θ) = sec2 θ - cos(2θ) - 1, (0,…

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Q: Use Linear Approximation to estimate Aƒ = f(3.02) – f(3) for f(x) = sin(). (Use decimal notation.…

A: Given: fx=sinπx16 We need to estimate ∆f=f3.02-f3 using Linear Approximation.

Q: Find the integral. Show complete solution. sinx -dx 1+sinx 3.

A: NOTE: You posted multiple questions, we have given an answer to the first question, if there is a…

Q: . Find the area of region between two functions fix)=sinx, g(x)-cos2x,-끌sxs을 %3D

A: The area between two curves A=∫abf(x)-gxdx sinx=cos2xsinx=1-2sin2x2sin2x+sinx-1=0sinx=-1±1+84=-1,…

Q: The area between y= 2sinx and y = sin2x for 0<x ST is

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Q: + Bsin z Differentiate @ wi th xespect to x - - S"d (use dy A sinz + B cose

A: Given that: y=Acosx+Bsinx

Q: Find the integral m tanx X, 1+x?

A: Given :

Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

Q: Use integration by parts to prove the reductionformula.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 9. f(x³ - 4x)dx -3 (x²-1) dx 10. ₂

A: We have to find the integral

Q: Use substitution to find the indefinite integral x +2x dx x4 + 4x² = 3 x+2x dx%3D x + 4x² - 3

A: We have to solve

Q: Explain how the Fundamental Theorem of Line Integrals and Green's Theorem are both similar to the…

A: Statement of fundamental theorem of calculus:

Q: Find the integral of * dx 2 sin x – cos x - |tan + 2 + v5 + C tan + 2- V5 In | tan + 2+ v5 |tan + 2…

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Q: Use Trapezoidal Rule with (n- 4) to find the integral dx x-1

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Q: integral of sqrt(9-x^2)(x)dx. limits are from 0 to 3

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Q: What is meant by indeterminate integral

A: Definition: An improper integral is the limit of a definite integral as an endpoint of the…

Q: 7. (x² - 2x + 3)dx 5²

A: SOLUTION-

Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy %3D

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Q: Integrate the function. 2+81 dx 4x2 V In Vx2 + 81 + x x2+81 4x + C In Vx2 • 81 + x] Vx2 + 81 + C 4x…

A: Given,            ∫x2 + 814x2 dx

Q: Expand Fourier function inthe rauge Co) %3D

A: Given that f(t)=cos2t where the period is π2. The fourier series is of the…

Q: Explain the application of triple integral in detail ?

A: Triple integral is used to find volume. For volume there should be three dimensions that's why by…

Q: -f integration for

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Q: Integral of tan^4(x)sec^6(x)dx

A: Sincesec2x=1+tan2xTherefore,

Q: Vx - 2 dx

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Q: Integral of 2cos^2x+3sin^2x dx from 0 to pi/2

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Q: = tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

A: 1-1cosh22xUse the Hyperbolic identity:  1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

Q: Integral of cos2x on [0, infinity]

A: We have to use limits to find the given integral.

Q: Find the integral of * dx J 2 sin x – cos x tan + 2 + V5 + C tan+ 2- V5 V5 |tan + 2-V5 V5 In tan+ 2+…

A: Option 2 will be correct choice.

Q: Which of f (x) = x sin2 x and g(x) = x2 sin2 x has a larger average value over [0, 1]? Over [1, 2]?

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Q: Prove dx dx 1 f ( sec -x+tan –I 2 1 | f (cosecz) %3D Vsin r sin x

A: Apply trigonometric properties to prove the result.

Q: Give examples of basic integration using reciprocal rule

A: Reciprocal rule of integration: ∫1xdx=lnx+C

Q: Hiwiy Express the ballowsing functions by Palar equationft 2.

A: To change a rectangular equation to a polar equation just replace x with (r cos θ ) and y with  (r…

Q: Evaluate the integral. HINT: [Use a shortcut.] e3x - 1 dx

A: Given integral: ∫-22e3x-1dx Substitute u=3x-1 and differentiate it w.r.t 'x'…

Q: Integrate ing with res pect to x; +8 - (3x+2) - the followi Sin (x) + + 2 4x dx 4 5x

A: Formula : 1. ∫xndx=xn+1n+1, n≠12.∫(ax+b)ndx=(ax+b)n+1a(n+1)3.∫1xdx=lnx4.∫sinx…

Q: Use Linear Approximation to estimate Af = f(3.02) – f(3) for f(x) = sin(). (Use decimal notation.…

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Q: find the most general ntiderivative f(x) = 4 sec2(x) + 3 sec x tan x

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Q: Q/Evaluate Integral:- sec2 3x dx tan23x-3 tan3x+2

A: To evaluate the integral:

Q: Find the absolute extrema of the function on the closed interval. y = 9 cos x, [о, 2л] (x, y)…

A: Given,

Q: Sudv= 2x)dx can be evaluated using integration by parts of the form v=uv

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Q: What is the Fourier transform of the one-dimensional rect function rect(x) = 1, for |x| |x|…

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Q: Evaluate functio J dx x² - 6x + 13

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Q: find the area of the shaded 4) reglon y = 2 2- y = 2 sin(Tx) 3 х -1- -2+ -3+

A: From the given graph the shaded part is on the interval x=0.5 to 2.5.  So find the area between the…

Q: integral of sec^4 (x) tan^2 (x) dx

A: Definition used -                                sec2x=1+tan2x…

Q: 7 (x +7) In@) dx

A: