CT/4 (x³ + x* tan x) dx J-7/4

Q: integral: 5x sec2 (x) dx

A: ∫ 5 x sec2xdx

Q: x´ tanh x f (x)= tan -1 (x)%3Dtan 2 sin x+ coS X

A: This is a problem of Differential Calculus.

Q: tan"x jun's de - | tan"-x dx (n 1) n- 1 tan x sec" r sec x dx (n 1) n- 1

A:

Q: 16. etan (1) sec² (x) dr

A:

Q: 3.sin (2 4. (4 sin 3x - x) dx

A:

Q: (tan x) = fu. v dx = (sin x) = | -=-=dx = (cos x) = fe" dx = | (arcsinx) = sec x tan x dx = secx tan…

A: We have to find out derivative and integral

Q: ON 3 sec3(In x) + sec2(In x) tan(In x) 2х n x) tan(In x) n x) dx c³(In x) + sec²(In x)

A: We have to choose the correct option according to the given information

Q: sec (In(x) 1. dx 2. Se tan(2x) sec²(2x)dx

A:

Q: sin Inx 12. S dx x cos² In x

A: Given integration is ∫sinlnxxcos2lnxdx We solve the integral using proper substitution.

Q: 4. Interval 0<x<n, function, f(x) = sin 2x. %3D

A: We have to find the Fourier series of the function fx=sin2x ,x∈0,π

Q: Prove the reduction formula

A: To prove: ∫tankx dx=tank-1xk-1-∫tank-2x dx

Q: Integrate √2 2 | sin x 2 √1-x² dx

A:

Q: sec x2-1 1

A: Given problem:-

Q: lim cos2x-1/sinx x-> 0

A:

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

A:

Q: tan°(x) sec²(x) dx = 1/7tan^7(x)+1/9tan^9(x) %3D

A:

Q: | sin x (3cosx)dx 2: VZ 3x dx V1- x4 3:

A: SOLUTION-

Q: Integration of b/1-sinbx dx

A:

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

A:

Q: x' sin (tanx*) -1 Integrate 1+x

A: Introduction :

Q: 1+ tanx log prove that = sec2x dx y 1- tanx

A: Giveny=log1+tanx1-tanx

Q: sin (2x) dx 2. ( (sin(In x) + cos(In x)]² dx xp: 3x/10 In(3x) – (1In(3x))²

A:

Q: sin x dx 1- sin2 x 4. cos x dx 2+3 sin x 5.

A:

Q: Using suitable method, show that 2 tan" (x+2) dx =- – In 2 .

A: We use integration by parts to find integral tan inverse x.

Q: lim * In(sec(2x)) x→0 (sin(3x))³

A: To find the limit.

Q: (5) sinh 2x = 2.sinh x.coshx %3D

A: (5)To prove the following identity sinh(2x) = 2·sinh(x)·cosh(x)

Q: sin(5x) dx 2+сos(5x) اخترأحد الخيارات х + tan(5x) + с.ао —In | 2 + сos(5ӕ) | +с.Ь 1 +c.c 2+сos(5ӕ)…

A: Since , in the given integration problem we have derivative of denominator in numerator so we will…

Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

A:

Q: = 5 sec x tanx %3D

A: Please refer to the image below

Q: [sec² x (1 + tanx) Vtan² x – 9 tan* x| dx

A: Formulae used:…

Q: eCoS ecos x sin x dx In x 2. Vx 3. tan'x dx

A:

Q: sin 2x+sin x dx Vsin2x -cos x v.

A:

Q: 9. S sec³ x tan x dx

A: Given ∫sec3xtanxdx We know that  ∫secx.tanx=secx + c ∫xndx=xn+1n+1+c

Q: integral sec^5 x tan x dx

A: we have given that ∫sec5x.tanx.dx

Q: tanx 4 – lim 0 Cos[1– –] X 0.7 O 1.5 O 0.5

A:

Q: i) Integrate  f sin 3x dx                                                                       ii)…

A:

Q: 2 X (x-sinx)2 | 6x'sin² 2 3/2 - Evaluate: +3x dx. X, X-sinx

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Q: integral (x-1)sin pie x dx

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Q: cos x sin x dx 4. sin 2x cos 2x dx 5. cos x sin* x dx 6. sin 3x dx 7. sin³ x cos? x dx 8. 3.

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Q: )etan²x f'(x) = (tan² x)et %3D Option 2 g tan?x f'(x) = (2 tan x)e

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Q: integral cos -1 x dx

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Q: Q/Evaluate Integral:- sec2 3x dx tan23x-3 tan3x+2

A: To evaluate the integral:

Q: 9. sec(1- x) tan(1 – x) dx

A:

Q: separable 9-X(2lnX+1) Sin y+ ycosy

A:

Q: sec² x 12. S 1+tanx

A: here we use       ddxtanx=sec2x see below the calculation and answer s

Q: etan x dx 1 – sin²x

A:

Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step

Q: integral sin -1 x dx

A: Given Data The integral is ꭍsin-1xdx.   Let,

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.