2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x sin(nx)dx 1Y- cos(nx))_(2+-sin(nx) cos(nx) -4T

Q: 1. Integrate: [x³ sin(2x) dx.

A: As per Bartleby guideline, only the first question has been answered. If you want to get the answer…

Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos…

A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 .

Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

Q: dy + sin 2x + sin 2y + 2 sin 2x sin 2y dx solve by Separable method

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Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

Q: Find the intergration of x^3(x^4-sine)^5 dx

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Q: |2tan x In (cos x) dx=

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Q: Solve Cauchy Euler DE 4x^2y"-4xy'+3y=sin ln(-x), x less than 0

A: Let t =-x >0. Then the differential equation       4x2y''-4xy'+3y=sinln-x becomes…

Q: 10. | [3 - e-lxl – cos x + log(x²)]dx = 0 x³ +4x – sin x 11. x² – 7 -dx 3 0

A: 10. ∫a53-e-x-cosx+lnx2dxEliminate absolutes =∫a53-e-x-cosx+lnx2dxApply the Sum Rule:…

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

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Q: Q1/Prove that S cosh(2x)sinh(x)dx = cosh(3x) – cosh(x)) -

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Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: 4. S(cos 2x)e$in 2.x dx 5. S cos x In(sin x) dx 6. ſ tan 0 In(sec 0) de

A: According to given : Only 4,5,6 are solved

Q: 6. sin'x dx 7. cos*x dx 4x+ 2 dx x +x + 5 8. .2 (1+x*)dx 2x-1 dx 2-8x + 15 10. 2x+x +1 1. dx (x-1)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Integral of sin^3 x dx over cos^4 x

A: In this question we have to find the Integration.

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: 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: (b) Prove that 1+ cosh x + cosh 2x coth x sinh x + sinh 2x 1+ cosh 2x + cosh 4x dx Hence evaluate…

A: 4b. Given,

Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the CRITICAL VALUES of f(x)=sin² x+cosx on the interval (0,2n)

A: Critical points are the points where the derivative of the function is zero or undefined. Our…

Q: Find the differential equation of the family of circles with centers on the line x – 2y = 3 and…

A: Given:  circles with centers on the line x – 2y = 3and passing through (3, 0).

Q: y" + 2y' = sin 2x ||

A:

Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

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Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: integral of cos x sin^3 2 x dx

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Q: Plot f (x) = ln x − 5 sin x on [0.1, 2] and approximate both the critical points and the extreme…

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Q: 2. Integrate using Trig: cos° x dx

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Q: [2 2 sinx cosx + 3cosx7 2 cosh 3 X 1 D²+ 4 D3 D³ -27

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Q: (7) Find if \.Y =ln12- Cosx) , 2- Y= %3D

A: Calculate dydx. 1. y=ln 2-cos x. Derivate with respect to x by applying chain rule: dydx=dydududx.…

Q: Show that sin(x^2) ≤ sin x for 0 ≤ x ≤ 1. Deduce that sin(x^2) dx ≤√2/2 on the invterval [0, π/4]

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Q: Use Variation of Parameters to solve the differential equation. y"y tanx y C1cos xC2sin x - In secX+…

A: Result used:

Q: First and second derrivative of: y=5 /(sin 3x+cos3x)

A: the given function is: y=5sin3x+cos3x we have to find the first and second derivative of the given…

Q: 1. Integral of x sin^3 (x^2) 2. Integral of sin^4 3x

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Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

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Q: 57 ves y sinx and y=cosx from x=- to x=- 4 4

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Q: Particular Integral for the differential equation (D² + 25)y =(cos5x) is given by a. -xsin5x 5 b.…

A: Option; b is correct.  Given differential equation ; (D2  + 25 )y  = cos5x Let D = m; Auxiliary…

Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b.…

A: Here we have to transformed the given integrand.

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

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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: (0)3-3x+2 sinh' (In x) cosh (In x) (E) sin(2x)dx dx N

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Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

Q: Integrate: [ sin³ 3x cos5 3x dx [sin³ 3x cos³ 3x dx = [ {ITEM D1} dx = [((ITEM D2]) cos5 3x sin 3x…

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Q: Find the differential equation of all family of circles in which the center lies on the line y = -x…

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Q: 4. S tan x dx CSC X sec (In x) dx 5. dx 6. S; 1- cos 2x

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Q: 2. f x cos² x dx

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Q: The solution to the differential equation -y x cos(3x) - is: Select one: cos(3x) + cx2 O 3x² sin(3x)…

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Q: integral from 0 to pie over 4 of sin^2 (4x) cos^2 (2x) dx

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Q: 3. SIX f- - dx x in x√√(inx)2-9

A: