(x²–1)dx S (x++3x² +1)[tan-1 x2-1 aluation of is

Q: Find dy/dx for the following : 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin-1 5x)…

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Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

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Q: (a) [(0.6e15 + 4t 3t² +03-10-01 at 4t4-3t3 + 0.3 _10t 1.5 -0.1 2t3 (b) Evaluate…

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Q: 1-) dx dx n above is separable.

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Q: Find the Absolute Extremum of F(x)=2sinx-cos2x over [0,2pi]

A: Consider the following:  Differentiate the function and find critical point:…

Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

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Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: 68) Find a value of c that will make sin2 4x 0 x2 f(x) = C, x 0 continuous atx = 0.

A: Given,

Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: B: 3:Use Gamma & Beta properties to evaluate : f (In x) 3 dx

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Q: 3+9sin' x Evaluate dx using suitable technique. cos x

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Q: The minimum value of cos x + 3 sin x + 5 is: - V10e A 5 - V10- в 5+ V10 D -5 - V10

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Q: 1 Evaluate [ (x³ +cos(3x))dx 2

A: The given integral is ∫x3+12cos3xdx.

Q: dx Evaluate x²/4 x²

A:

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: (4) Evaluate cos (2x) -dx. (x² + 1)² 8.

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

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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: (a) Show that cos(x²) > cos x for 0 ;. 1

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Q: Evaluate D³(sinx - 4e²x) A -sin x-32e²x B -cos x-32e²x (C) с cos x-32e²x D sin x-32e²x

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Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: 6 Evaluate (a) [ a + (4x-2° dx + (4x-2)* dx (2x-3)2 2x sin (x²+!) cos (x+1) dx

A: AS mentioned by you that "none of these is graded please answer 5. These are practice questions"…

Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: Find the root of f(n) = 3x - cos(x) -1 = 0

A: Please rate and feel free to ask any query about any part.

Q: 1. S(tan -1) dp 2. sin2 B cos ß dB 3. S: xdx -7-8x-x

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Q: The integral / 2' )cos(2*) dx takes the form k cosu du when u=2* and f (x) =x- 5. What is the value…

A: we use the formula ddx(ax)=ax lna

Q: 1. / 2dx 3D 0 + С %3D С 2. Sx²dx = 2x + C %3D 3. S 5x*dx = x5 1 4. Sdx = + С 2(х2-5) x2-5 5. ſ tan x…

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Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

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Q: f(x) = cos (In (3x))

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Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

Q: 6xsec 3x 2-If y = (tan3x)²² prove that = (tan3x)²= + 2ln(tan3x) %3D dx tan3x

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Q: Find dy/dx of y=sin -1(1/x). (A x²– 1 3 B 1- 9x2 1 9 D 1-x2

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Q: (一 - dx t - 3 X*cos(3)-4-2 ) -)dy=0 = 0

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Q: If y = x tan-x- In /1+ x² then ¬1x-In V1+ x² dy is dx

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Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: Q3: Find lim,- (2 – sin –) إجابتك :Q4 For (3x³ – 5x) V2x+1 find dy/dx at x=0 إجابتك

A: Explanation of the solution is given below...

Q: 1 a) 1+ sin(x) xp- Vtan (x)dx

A: a) Given integral is ∫11+sinxdx

Q: 0<x<T (-1)"-1 f(x) = { 27-x COS nX n<x< 27

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Q: Use graphs to evaluate 2π S 2r S 0 sin x dx = cos x dx = 2t S 0 2π sin x dx and cos x dx. 0

A: We will find the required.

Q: d21 0 is sinh(a) dx21 at x = 0 is

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Q: Q2- Find for the following functions :- dx 1- y = (Inx)/tnx 2- y = x cos-1 x - v1-x² +sin-1x

A: We have to find dydx for the following functions... 1. y=lnx1lnx2. y=xcos-1x-1-x2+sin-1x

Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

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Q: Find [(1 - cos² t)dt]. dx A. sin²x B. -sin²x C. 1 - sin²x D. - cos²x

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Q: Evaluate tan-1 x dx А. 1. tan-x dx = x tan-!x-;In(1+x²) + C В. 1. tan-x dx = x tan-x+;In(1+ x?) + C…

A: As we know that the expression for the integration by parts: ∫udv=u·v-∫v·du Given: I=∫tan-1xdx or…

Q: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

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Q: proximation at z = 0 to sin(4r) is A + Bx where A is:

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Q: let's consider the equation (2xy - sec2 x) dx + (x2 + 2y) dy = 0

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Q: alue of A can be calculated based on f(x)dx = 1.

A: The given probability distribution function is,