Q3- Find: 1- Sv2 + sin3x . cos3x dx. 2-5* dx x5-2x sin 2x 2 sin x 4- f cscx cot x dx 4 cos x 5- S 3+ 2 sin x

Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

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Q: 3. S. 2 cotx-3 sin²x dx sin x 4. (2x2+x dx x+1

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Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

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Q: ... at verifies the identity. OC. B. sin 9x cos 7x - cos 9x sin 7x = sin (9x – 7x) = sin 2x sin 9x…

A: Given query is to find the correct option to prove the identity.

Q: aluate 9/ sin(x) cos(x) dx by four methods.

A: Here we want to perform the given integral according to each of the methods mentioned.

Q: I. Find dy -and simplify the result whenever possik dx 1. у%3Dsec3 2х - 3sec2x 2. y = sin (x + 4 )…

A: Given; 2) y=sin(x+4) cos(x-4) 3) y= -3 cot5(x/3)/5 + cot3(x/3) -3cot(x/3) - x.

Q: Q1|| Integrate SIX of the following functions: sinh(Inx)dx 1) 3) f 2) | ex.sinxdx sin (2x).cos(3x)…

A: As per bartleby guidelines we only give first three questions answers.

Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx…

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Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

A: Solve by differentiation

Q: Q No 4) Integrate S cosec³xdx . AND also Find F sin10xdx

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Q: csch (2 sin2x) dx 1. V1-4x² r(²-1)cos[cosh (In r)]dr OS 4.

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Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

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Q: f'(t) = sin 8t - cos -/-

A: You are correct

Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: 3. f(x,y) tanx - sec²x - cosy

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Q: Ssin x x cos x dx = %3D Select one: а. -cos 2x +C 4 b. -cos x + C 4 c. -sin 2x + C 4 d. -sin x + C 4

A: We need to evaluate the following integral ∫sinxcosxdx

Q: followin COSX 3. f- dx 1+sinx 4. f (sinx + cos x)² dx 203 (y² +1) 20 dy 5. f

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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: Find the solution of the equation in the interval 0"sx <360 1. cos x+) 3 = - cos x +T3%3D

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Q: The position of a particle moving along the x-axis is x(t)  = sin(2t) - cos(3t) for time t>= 0. When…

A: Given the position function, x(t)=sin2t-cos3t

Q: Find the most general antiderivative of the function. f(x) = 5 cosx-7 sinx

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Q: Find sinh + C sech V5 + C sinh () + C X. Cosh 5 O -1 csch--

A: Integral of the given function is -

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

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Q: rIn 2 cosh x dx. Vsinh a x + 4 sinh x +2

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Q: Describe the method used to integrate sinm x cosn x, for m even and n odd.

A: Method to integrate sinmx cosnx ,for m even and n odd. Let m=2k and n=2k+1 ∫sinmxcosnx…

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: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Differentiate f at x = 0.5 using 5 point formula. Also…

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Q: dy =Cos x Sinx cotX 8-

A: As we know that; The standard form of the linear differential equation; dydx+Py=Q Where P &amp; Q is…

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

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Q: 1 -dx= cosº x/2sinx 5 /tanx+=Vtanº x + C А. Vtanx+/tan5x+C 1 B. tanx +÷Vtan° x +C С. 2 2 tan x +C 1…

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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: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Show: 2 x + 2 sin dydx + 2y 1 va sin-dydx = 4 2y 2 va

A: The question is of change of order. First we need to identify the region formed by limits of…

Q: cos²x sinx dy + (y cos³x − 2)dx = 0

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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: 37. cos 6x dx 40. sin x? dx 39. cos do 42. tan x sec² x dx 41. sin 2x cos 2x dx csc2 x dx cot x sin…

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Q: FIND dy/dx FOR EACH FUNCTION. 1. y = (tanx + sinx)-3

A: 1). Given y=tanx+sinx-3. To find: dydx Solution: Power rule of differentiation states that:…

Q: Find sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

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Q: 3T 2cosx dx 1+(sinx)2 2 a)2 tan-'sinx|| b) 2 In sinx| c)2 In(1 + (sinx)² 2

A: We know that integration of 1/(a2+x2) is (1/a) tan-1(x/a) +c. Here' c 'is constant. Here i attached…

Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: b) By using integration parts, show that ii. S(3x + 5) sin(2x + 3)dx = -÷(3x + 5) cos(2x +3) +sin(2x…

A: By using integration by parts, show that∫3x+5 sin2x+3 dx=-123x+5 cos2x+3+34 sin2x+3+C

Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: 29. (csc x – sec x)(sin x + cos x) dx find + In 5 ) dx 30. 3 sinh .3 2x3 V1 + x² sin x dx 32. 31. dx…

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Q: Test for homogeneity

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Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

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Q: Find when 4= SINX Thuen dy (sinx) (ar f(s wheve for 0<x< M2 tanx taux a=?

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.