Which option equals Sx sec2x dx ? Exactly one option must be correct x secx tanx - In(cosx) + C O x tanx + In|cosx| + C x tan2x - In|cosx| + C O x tanx - In(cosx) + c O None of the above O

Q: 1 tan(x2)dx + 2 x2 =- sec?(x³)dx: 4 Select one: O True O False

A: We have been given the integral ∫01tan(x2)dx+2∫01x2sec2(x2)dx

Q: 2. Suppose, f'(x) =2 cosx+sec x, -7<x<: and it is known that f()= =4. Find the function f(x)

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Q: 3. Differentiate. SET A. y = 3 cos(5x2 + 2)

A:

Q: If f(x)= cos (x)+3x , what is f'(x) ? COS O f'(x)=-sin (x) +3

A: First option is correct. Explanation is given below....

Q: Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 1/4 3/8

A: We have given  ∫x sinx cosx =fx sin2x-gx cos2x+C Let,  I=∫x sinx cosx dx I=∫x sin2x2dx I=12∫x sin2x…

Q: d Select one: æ(sin=! æ)* 3x + 2 sin- x 3x x(sin x) -1 + 2(sin-1 x)? 1-a2 x² (sin-1 æ) 3(sin1 x) +…

A:

Q: 7. The value of A. cosx - C O A O B О с O D dx √(1-x is B. sin '(x)+c C. cosx ' +2¢ D. cosx

A:

Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: Evaluate: Sv*+sin/x dx. A x+2cos/x+ C 2x+ cosx B + C 2

A: We have to solve the integral

Q: What substitution should be used to solve the integral O sin u=3x/2 sec u =2x/3 sec u =3x/2 O tan u…

A: We have to solve the integral

Q: Find f(x) given that: f'(x) = 2 cos x -3 sin x and f (주) %3D %3D

A:

Q: 2. Extend the identity cos(ax)-cos?x-sin'x for xE PR to the identity cas (a2)- Cos s 2-sinz for & €…

A:

Q: Using an appropriate substitution, f sin³ (x)cos®(x)dx is equal to: sinx + C sin13x + C 13 sin11x…

A:

Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: y=x-2cosx Differentiate the function. dydx=ddx(x-2cosx)=1+2sinx

Q: Evaluate: /x?cos(2x)dx 2x2sin(2x) + 2xcos(2x) – sin(2 x) А + C 4 2x2sin(2x) – 2xcos(2x) – sin(2x) +C…

A:

Q: Evaluate the given function tan²ydy = sin3 xdx is equal to.. 3(tany – y) 30 + cosx А. Зх - cos³x…

A:

Q: Evaluate the given function tan?ydy = sin3 xdx is equal to. 30 3(tany – y) А. Зх + cos³x = cosx cosx…

A: tan2ydy=sin3xdxIntegrate both sides and solve.

Q: The sin(5x + 2x) dx cos5xcos 2x is equal to 2 In(sec 5x) + 5In(sec2x) +C А. 10 In(sec 5x) +…

A:

Q: If f(x) = sin?x, then f"(x) = %3D A 2cos2x B cos2x -sin2x D -4sin2x

A: Given, f(x) = sin2x For the given function , applying chain rule ,  First differentiate it as { xn ,…

Q: III) Prove: 2) cos x x + sin æ sin y = sin 3y (3) COS (2) for all x and y such that x+y= 2

A:

Q: x is in the interval [0, 2t) * sin2x - cos2x = 0 COS

A: Given: sin2x-cos2x=0; x∈[0,2π) We know that cos2A-sin2A=cos2A…

Q: The suitable substitution to evaluate sin24(x+2) dx is None 1 [1- cos4 (r+2)] [1+ cos8(r + 2)]…

A: Topic- integration

Q: Compute tan" z · sec² æ dæ. O tan12 z tan10 z +C 12 10 O tan° a tan10 a +C 10 tan12 a sec æ +C 3 12…

A:

Q: Which option equalsS x sec2x dx ? Exactly one option must be correct x secx tanx - In(cosx) + C O x…

A: Hence option (b) is correct.

Q: If f(x, y) = x³y + cos(x) then (fa, fy) = (3xy - sinx, x³). Select one: O True O False

A:

Q: 28. Evaluate f 5 sin 3x dx 2+cos 3x a. 2 In 15 sin 3x| + C b.- In 12+cos 3x|+C c. In 15 sin 3x| + C…

A: Evaluate integral

Q: by implicit di f foretiation of sin-(xy) - cos-(x- y) Find -V1- (xy)? xV1-(x- y) ² + V1- (xy)? -V1-…

A: Using Implicit Differentiation

Q: Evaluate: / sec (5x + 1).5dx Select one: O cor(5x+1) + c O tan(5x + 1) + c O cor(5x) + c O tan(5x) +…

A: Use the substitution method and simplify the given integration than integrate.

Q: What is the multiplicity of the zero p = f(x) = 2 – 2 cos x? of Select one: 1 2 3 4

A:

Q: Which of the following tables has been completed correctly using exact values? Cos x sec x 0°…

A: We are required to find the value of sec x and cos x for different values of x between 0 degree and…

Q: 25. fx sec²xdx is a. x tanx - In cos x b. x tan x + In cos x c. x tan x-sec²x + C d. x tanx+sec²x +…

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Q: 6. Which of the following is FALSE? 7. f A. (4 cos x-3 sin x) dx = 4 sin x + 3 cos x + C B. f3e³x dx…

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Q: TO For x such that 0 < x<, the expression 2. V1-cosx V1- sin'x COS"X is equivalent to: sin x COS X

A: I am solving this in step 2

Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

Q: х Given that t= tan , show that: 1-1? 2t d) sin x = 1+t? e) cosx = 1+1? 2t f) tanx = 1-?

A:

Q: dy Find , if Y = (1+ cosx)sinx dæ cos3x + cos³x – sin²x O cosx + cosx – sin³x cos2x + cos²x – sin?x…

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Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C

Q: Evaluate: a sec a tanxx dx from a = 0 and b = O 12- 1/ 0용 + 1 O none of these O v2+ 1

A: Given query is to eveluate the integral.

Q: Q3:A| Prove that:- cos x 1) 1+sin x 1+sin x = 2 sec x cos x tan? x 2) tan? x+1 = sin x

A: topic - trigonometric identities

Q: The f sin x cos²xdx is x sin 4x {A} 16 64 sin 4x x {B} 16 16 O A B O - sin³2x 48 sin³2x 48 +C + C…

A:

Q: Find r (3) /" (종), /" (주) , f' (), ), fm given f (x) = sin a cos 3x

A: Given: fx=sinxcos3xf'x=cos4x-2sinxsin3x To find: f''π3=?f'''π3=? Formulas used:…

Q: The suitable substitution to evaluate | sin² 4(x + 2) dx is None O A. - cos8(r +2)] [1- cos4(r+ 2)]…

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Q: Q4: Prove that: cos?x – sin?x = 1- tan?x cos?x

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Q: : s ech[In cosx]tanx dx Evaluate: A None - 2 tan-1(cosx) + C 2 tan -1(e cosx) + C CoSx (D - 2 tan…

A:

Q: Consider fx sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? O 1/4 1 O…

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Q: O Find the solutions of : 1+sinx=2(cosx)´ in the interval 0<x<2T.

A:

Q: Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x ,…

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