aluc of 4 alue of dx. 1+(x – 2)? 1

Q: 9. cosh x + sinh x= e* %3D

A:

Q: 3.3 Inx + tanxe d 4-4x -sinte dx

A:

Q: 9. cosh x + sinh x = e* %3D

A: To Prove,                cosh x+sinh x=ex

Q: nction 'a' is 1+eaz at its pole

A:

Q: (2 cos z-sin z)² dx Evaluate sin z

A:

Q: 24 dx Evaluate 1- cos (8x) 24 dx 1- cos (8x) | I3D

A: Using trigometric identities

Q: 5. Evaluate dz (sin(x*)).

A:

Q: (3cos³x-1 1- sin?x To evaluate - dx the integrand can be transformed to [(3cos³x + csc?x)dx |Зcosx…

A: Option D is the tranformed integral.

Q: ropriate substitution, n³ (4x)cos*(4x)dx is equal to

A:

Q: dx Evaluate x²/4 x²

A:

Q: S sin² 2xcos² 2xdx

A: This question is based on indefinite integral using Trigonometric formula.

Q: 3cos3x - 1 To evaluate dx, the integrand can be transformed to 1- sin?x

A:

Q: Evaluate x dx Sin odo 2-X

A:

Q: sinh?, sinh x + cosh x dx - cosh? 2

A: Evaluation of the integral

Q: arctan(x) dx = x arctan(x) - 2 In(1+ x?) + c

A:

Q: 1 Proof (I): (sinhx)' = Vx? +1

A: Given: The equation is sinh-1x'=1x2+1. To prove: The main aim is to prove the equation. Concept: The…

Q: . Scos(In x) dx

A: Formula used in integration by part   ∫ fg' = fg -  ∫fg'

Q: integral Scos 4 (3x) Sin (3x) dx Evaluate the

A:

Q: YOUR TURN 6 Find xV3 + x dx form Sub In be 1. 2.

A:

Q: 6. y = -sin (²x) III Thre KIN 플 X

A:

Q: ‚arcsin(1+x²)] y'of y = In cscya

A: Given y=lnearcsin1+x2cscxWe need to find y'

Q: 1+ xcosx Evaluate: dx x(1-xe 1-re? sin x

A:

Q: Antiderivative of sec(3x)tan(3x)

A:

Q: N = 3 tan-(x)dx

A: Here we have to evaluate I=∫033 tan-1xdx.....................................(1)

Q: A) Find the nearest distance from the point (-4,2) and the line 2x-y 5 dzy dy and dx B) Find if x =…

A: A) The nearest distance from any point to the line is always a length of the perpendicular from the…

Q: sin (x) dx 4 3 2/38 1/3 4/3

A:

Q: 3. S tan¯¹ √√x dx

A:

Q: 3cos3x (3cos³x - 1 1- sin?x To evaluate dx, the integrand can be transformed to

A: Given: - The integral is, ∫3cos3x-11-sin2xdx To find: - The given integrate can be transformed to.…

Q: I. Power Formula sec² xdx 1. S (1–4tanx)7 (2x+1)dx (x+2)*(x-1)* 2. S;

A: In this question we have to find the following integral using power formula. We know, Power formula,…

Q: ( 3cos³x-1 To evaluate the integrand can be transformed to 1- sin?x O [(3cosx - sec?x)dx o f3cosx (1…

A:

Q: Integral of 2cos^2x+3sin^2x dx from 0 to pi/2

A:

Q: 1+ax ). dx Evaluate 1-ax

A:

Q: 1 Evaluate – -dx 1+ 3sin"x + 8cos™x

A:

Q: tan" -1 I# Z-X FEMD fyx At (-,1).

A: The solution for the above question is as shown below.

Q: Scoth (2) dx

A:

Q: 3 sinx+cos x Evaluate S dx. 2 sinxcos x

A:

Q: 0sin 2 x coOS x dx

A:

Q: 1 dx ½ x* -1 1 a) arctan -In 3+ 3 4 8 1 b) -arctan 3 --In 2+ 3 4 8 c) -arctan 3 +-In2+ 4 8 1 1…

A:

Q: O IT 3 tan'z sec z dx

A:

Q: 5. sin n° x cos x dx >

A: The question is taken from the calculus in which we have to find the value of the given integral, We…

Q: 3 dx 23.

A: Given:

Q: cosh 3 хр. 15) 1-sinh 3

A: Solution

Q: [(2sin x + 3cos.x) dx

A:

Q: 6sin³ (2x) cos(2x) dx =

A: the given indefinite integral is: ∫6sin52xcos2xdx we have to find the value of the given indefinite…

Q: 3 sin x d.x 4 1. Show that

A:

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

A: The given probability distribution function is,