Evaluate /(e* + - + cos4x)dx O + logx + sn3x +c e2r 3 4 e3x sin4x + logx + + c 3 2 O + logx + e5x 2 sin3x + c 5 e3x O + logx + 3 sin4x + c 4

Q: Determine one real root of 2x cos 2x - (x - 2)^2 = 0 on the interval (2,3) using Regula Falsi…

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Q: Determine and of y = (5r - })(cos z + In z

A: Consider y=5x2+32sin x+ln x. Calculate: dydx=y'. Apply product rule of derivative:…

Q: If e /2i =sin2 then z = 2i In(sin2) + 4k TI - 2i In(sin2) – 4k TI - - 2i In(sin2) + 4k TI - -2…

A: Use the principal log to find z.

Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: 1-In (-) + In(2x³) = In3 2- 4 log 2 – log3 + log16 = x 3-Expand In [x? sin3 x /Vx2 +1]

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Q: Express the product as a sum or difference. sin 6x sin 4x (cos 10x - cos 2x) O sin2 24x2 (cos 2x -…

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Q: 5) Integrate 2x cos (x²-5) with respect to x.

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

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Q: Evaluate the integral: 25 tan² 12x dx Choose the most appropriate answer. tan3 3 12x O 25 × 1 12 ln…

A: Explanation of the answer is as follows

Q: Find * sin (In æ) cos²(ln x) dx. cos (In x) , cos³ (In x) 3 cos (In x), cos³ (In x) 5 3 5 Option 3…

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Q: 256 cos(85 x) cos(32 x) cos(4x) dx = 64 cos(49 x) + cos(57 x) + cos(113 x) + cos(121 x) 64 cos(49 x)…

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Q: Prove cos 4x = 8 cos4x − 8 cos2x + 1.

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Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 + 8 8 sin(3x)cos(3x) , sin(2x)cos(2x)…

A: We need to evaluate integral.

Q: Verify the identity cosh2 x = (1 + cosh 2x)/2

A: We simplify each side using the formula of cosh(x)   Left side:

Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

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Q: Solve exactly over the interval 0 ≤  θ  ≤ 2π 1. √3 Cosθ- 2sinθ cosθ = 0 2. Cos(θ/2) - cosθ = 0…

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Q: (cos20+ jsin20)-3(cos50+jsin50)? (cis40) (5e/20)3 Simplify O a. 125(cos1460+ jsin140) O b.…

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Q: Prove | cosz |2 = cos²x+ sinh²y.

A: To Prove: cos z2=cos2x+sinh2y

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

A: topic- indefinite integration

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

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Q: 5. Compute Jo Jitvx 1 dx -2

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

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Q: Compute : exp(i sin(e-i))

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Q: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

Q: Evaluate. 2tan2120° +2sin2150° -cos20° 5sin2300° +csc2150° -sec230°

A: To Evaluate. 2tan2120° +2sin2150° -cos20° 5sin2300° +csc2150° -sec230°

Q: Find the indefinite integral. [ cos 3xar sin33- sin 3r +C 6. O sna(3- sn'ax) sin3 3-sn 3 +C sn3x…

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Q: Compute for a real root of 2 cos √x - sin √x = 4 accurate to 4 significant figures using Fixed-Point…

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Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: 292 cos(25 x) cos(108 x) cos(4x) dx = x)) dx O 73 cos(-86 x) + cos(-78 x) + cos(128 x) + cos(136 O…

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Q: 2. Show that by using MEAN VALUE THEOREM 4-n < tan-1 v – tan-1 u < 1+v2 if 0< u<v 1+v2 3 <tan 25 -14…

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Q: Find 2. dy of 2.

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Q: Compute ∫xsin(3x−2)dx.

A: Let the given

Q: The proper transformation for sin²x to make the f sin²x dx readily integrable is {A} 1- cos²x {C}(1-…

A: Given the query is to find the correct option of integral.

Q: Prove that ; cosec x . cosec 2x . sin 4x . cos 6x . cosec 10x cos 3x + cos 5x cos 7x cos 9x sin 2x…

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Q: Compute sin(sin( 3337 7 * ). -67 -57 7 -4T 7 -37 7 -27 O O O C

A: Computing the value

Q: (8) If fCx) = 3x*- +4X +1, Sind

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Q: prove tan^4x=cos4x-4cos2x+3/cos4x+4cos2x+3

A: Basic trigonometry proof

Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

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Q: Ssin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) , sin(2x) + + C 12 8 8. 4 sin(6x) sin(2 x),…

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Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

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Q: Compute sin (3r)dr (25z4+1)2 -

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Q: Find the derivative of f(x) = ecos² (3x+1) Of(z) 6 sin(3r+1) cos(3x + 1)ecos² (3+1) O (E) None of…

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Q: cos(9x) -dx COS J 1+ sin²(9x)

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Q: Suppose f(x) =cos ( 3x – 2). Evaluate: A -3sin(3x - 2)+C ® -sin(3x- 2) + C sin(3x – 2) +C 3sin( 3x –…

A: Given function f(x) = cos(3x-2)

Q: Evaluate the integral cos3 x + sin² x + 1 dx cos² x (sin2 x + 1)

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Q: compute:   ∫sin^3xcos^2xdx

A: We have to find:

Q: Prove that : 1. Sinhx= In(x+x² +1)

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Q: cos( 2 tan1 (x/ 4)) = Select one: O 2x ( 16 - x2 )0.5 / ( 2x2 - 16 ) O 2x ( 16 - x2 )0.5/ ( 16 - 2x2…

A: Solution:-.

Q: Evaluate: cos32xdx cos³2x - +C 6. cos2x (A) cos32x +C cos2x B sin2x sin32x +C 6. = 2 sin32x + C 6.…

A: Given query is to find the integral.