Which of the following is always true for integrable functions f and g? + g(x)]dx = / g(x)dx+ | f(x)dx A © /[s(#) – g(=)\da = / g(=)dx – / s(a)dz %3D f(x) dx S f(x)dx where g(x) + 0 g(x) T9(x)dx |[S=) • g(x)]dxr = / f(#)dx• / g(x)dz

Q: integral (In x) 3  dx

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Q: sin(x) + 2 x4 +1 5. Determine if the integral dx converges or diverges.

A: Cauchy integral test : For an>0,let ∑n=λ∞an is a series of positive  terms. Then ∑n=λ∞an is…

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Q: 3) f(x) = (x + 4) Standard form: Y-int:

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Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

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A: Given integral I = ∫sin2x sin 3x dx∵ cos2θ = 1-2sin2θ ⇒ sin2θ = 1-cos2θ2I = ∫1-cos2x2 sin 3x dx  =…

Q: n, ]x| fn (x) = - 2m 0, x > 2n | fn (x) cos x dx lim Calculate its limit. What happens if the limit…

A: Write the integral as limn→∞∫-11fnxcosx dx=limn→∞∫-1-12nfnxcosx dx+∫-12n12nfnxcosx dx+∫12n1fnxcosx…

Q: What are the new limits of integration if apply the substitution u = 6x + n to the integral sin (6x…

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Q: (5) Find the indefinite integral (a)f Vtan x sec²dx (b)fem2* sec² 2xdx sin x (c) Cos x 1 cos-do 0 2

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Q: Express the limit as a definite integral. n 7 lim 2 3x Ax: [2,7] Ax,0 k= 1 O A. 3x' dx 2 о в. 3x'd…

A: We have to express the given series as a definite integral.

Q: Decide whether or not the given integral converges.   +∞ 4 x1.5 dx   1

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Q: What are the new limits of integration after applying the substitution u = 5x + z to the integral s…

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Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 + 8 8 sin(3x)cos(3x) , sin(2x)cos(2x)…

A: We need to evaluate integral.

Q: Issol za 53. f(x) = VxIn x on (0, co) %3D

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Q: Express the limit as a definite integral on the given interval. lim n → ∞  n [2 − 5(xi*)2 + 6(xi*)4]…

A: Given query is to find the integral form of limit.

Q: Evaluate f x² cos 4x dx Evaluateſ sin* 3x cos3 3x dx Evaluate the integral J x²+x-1 dx x(x²-1)

A: Given:   i) ∫x2cos 4x dx      integrate by parts ∫fg'=fg-∫f'g     here f=x2,f'=2x , g'=cos…

Q: A scientist uses the one-point Gauss quadrature rule based on getting exact results of integration…

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Q: Verify the power rule for integration fx'dx= n+1

A: Given a power rule of integration,

Q: The integration expression sin(3In(x) + 4)cos(3In(x)+ 4)dx must be transformed into using suitable…

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Q: Find the value of* cos(x) sin (2x) lim sin(x) – 1 - O 0/0 4. O (intinity)

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Q: Find indefinite integral.

A: Let the given integral be y - y = ∫x12+3x-23 dx      Identity to be used - ∫xndx = xn+1n+1+C

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: Only one of these calculations is correct to evaluate the definite integral Inx dx Select one: 1 Inx…

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Q: Compute the integral (3)/(1+x^2)-sec(x)tan(x)+2^xdx

A: The given integral is: ∫31+x2-secx tanx+2x dx ∫31+x2-sec x tan x+2x dx=3∫11+x2dx-∫sec x tan x dx+∫2x…

Q: When we find the area between an upper curve f(x) and a lower curve g(x), we integrate f(x)-g(x).…

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

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Q: 6. S sin(ln x) dx 7. Show that x" In x dx = 山+ In x + C. n+1 n+1

A: Note: As per the company's guidelines we have to solve only one question. So, kindly post the next…

Q: What are the new limits of integration if apply the substitution u = 5x + n to the integral sin (5x…

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Q: 1- The point of intersection of the logarithmic functions on the X, Y axes =1. Why? 2- Are all…

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Q: Let u = x3 + 1. Indicate how the limits of integration should be adjusted in order to perform the…

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Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

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Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

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Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

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Q: solve the integral: I2=  integral limit from 0 to 4= 1/((x+1) squar root of 2x+1) dx

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Q: Integrate (three) of th 1) f sin6x cos3x dx 4) [x² (1+¹)4 dx

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Q: arctan(x) dx 2 + ex 20 Jo convergent divergent

A: Answer is convergent.

Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

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Q: Ssin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) , sin(2x) + + C 12 8 8. 4 sin(6x) sin(2 x),…

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Q: Match the integral expression on the left to an equal expression on the right. Ssin(3x)sin(4x)dx -…

A: Let's find.

Q: Match the integral expression on the left to an equal expression on the right. Ssin(ax)sin(4x)dx +…

A: We know that; The trigonometric identitites; a). sinxsiny=12cosx-y-cosx+yb).…

Q: Why is that the multiplication and division of the functions cannot be used in normal integration…

A: We have to give the reason that why the multiplication and division of the functions cannot be used…

Q: What are the new limits of integration if apply the substitutior u = 6x + t to the integral sin (6x…

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Q: f(x) = _-2x² – 6x – 4 х2- х - 2 Holes: Vert. Asy: Hor. Asy: x-int: у-int: Domain

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Q: What are the new limits of integration if apply the substitution u = 4x + t to the integral / sin…

A: We have to change the limit.

Q: integral In x 2 dx

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Q: 2. f x cos² x dx

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Q: Find the indefinite integral ∫ [arctan(x/2)] / (4 + x2) dx

A: ∫arctanx24+x2dx Now put, arctanx2=t⇒11+x22·12=dtdx⇒11+x24·12=dtdx⇒44+x2·12=dtdx⇒24+x2=dtdx⇒14+x2…

Q: 1 Integrate: S tan*÷x dx 3

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Q: 1. Find the numerical Integration of cos(x) + sin(x) where n = 4 using trapezoidal rule.

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Q: Use integration by parts to evaluate the definite integral: ∫3se^-4s ds with an upper limit of -0.9…

A: A=3∫abse-4sds , solving A where a,b are upper and lower limits as per questionIntegrate by parts…