d du 1) (sin-1u] dx %3D 1-u2 dx -1 du 리는 [cos-1 ul = dx V1-u2 dx d 1 du 3) = [tan-1 u] dx %3D 1+u2 dx -1 du 4)는 [cot-l u] = 5)을 [sec-l u] = %3D 1+u2 dx dx d 1 du %3D dx u vu2-1 dx -1 du 5)[ csc-1u] dx u vu2-1 dx

Q: What is the resulting integrable form after you applied substitution technique in tanx sec“x dx?

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Q: Differentiate. cosx² + siny³ = 36 %3D

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Q: dy Find ax for y = cosx(1 + cscx) dy O 1) = -sinx cscx cotx %3D O 2) 2) dx = -sinx(1+cscx)-cosx cScx…

A: Given, y=cosx1+cscx We have to find dydx

Q: sen z + cos x dz | (tag z + 1) dx = In sec x+z + C 37. %3D cos 2

A: 37.   Given integral, ∫sen x+ cos xcos xdx

Q: Find the integral of ∫tan^5(4x)dx

A: Given Data: Integrand: ∫tan54xdx   let u=4x   The derivative of the above equation is, dudx=41dx=du4

Q: Section 3.4-The product rule and Quốtiént rule In(x) Differentiate: Y dy Preview %3D dx

A: Given: y=ln(x)x9

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

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

A:

Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

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

Q: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

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

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Q: 2. dx Ix Also, Prove that 22 %3D dxdj = dy dX

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Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: What is the integral of question 23 and why is the answer 0?

A: Let f(t)= t^4*tan t/(2+cos t)

Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: 5 sin“(3t) dt

A:

Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: (雲) 1 dy tion 1+ is = 3 dx wy da 3, 1 12, 1 1, 15 15, 1

A: We have to choose the correct answer

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: what is the acceleration at time t=o of a particle if its position is s(t)= cos (3t)-sin(4t

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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: Integrate (three) of th 1) f sin6x cos3x dx

A:

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

A:

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

A:

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

A:

Q: Consider sin¹x cos³x dx. If we let u= sinx, the integrand can be transformed to

A:

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: sin(6y) sin(8y) dy.

A: Topic - integration

Q: 1+ tanx y = logy 1- tanx prove that 9 = sec2x dy dx

A: Given,           y=log1+tanx1-tanx

Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: 2. Integrate using Trig: cos° x dx

A:

Q: = Solve: Cony siny dx + dy. cosr sinx

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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: 3cos3x-1 uate f dx, the integrand can be tran 1-sin2x Bcos3x + csc²x)dx

A: We have to choose the correct answer from the given options according to the given information

Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: What is the integrable form of sin-cos-sin0 de 2 2 du 2 1– u² du cosu du -2 sinu du

A: To write the integrable form.

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

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Q: х2 9 dy + sinx - у %3D0 dx

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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: What is the integrable form of sin-cos-sine de? 2 2 V1-u? du -2 sinu du u² – 1 du 2/ cosu du

A: We have given integral Let, I=∫sinθ2cosθ2sinθdθ As, sin2x=2sinxcosx sinx=2sinx2cosx2 So,…

Q: 11 tanto-2 tan Bz1 show that 2 coste- Cos B20

A:

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

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…

A:

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: Exercises ESet 27 Implicit Diffexentia tion 2 1. Find dy if dX +Sinxy Find dy if 2x' 3y8 -2- dx2

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Q: (7 – siny)y' = 3x2 + 2x

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

A:

Q: find tan x dx x² x² tan¬' x dx 19. 20. sin 3x cos 2x dx 22. sin 2x cos 3x dx S sin sin 8 sin 4t sin…

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

A: