3 Prethat Sin x Tmprepenly Jx Tnteg rable (0,1)

Q: Si sin“ (3y) cos® (3y) dy 128 2340135 128 780045 O 9.64 x 10 4 O 2.89 x 10 3

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Q: 3. [(3t +r*)sin (21)dt /

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Q: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: (iii) 1 dø -sin²Ø Hint: may start with de (T(1/4)} /2 Vcose to obtain the result

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Q: -3+ Sin zt dt 7 8-1 i uct-1) } e-zt 9- to

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: If e /2i =sin2 then z = /21 - 2 In(sin2) + 4kTt – 2i In(sin2) – 4kt | 2i In(sin2) + 4k T - 2i…

A: We use the identity e^(2πki)=1 and by tanking ln both sides and then calculate.

Q: 2 6 Use Fubini's Theorem to evaluate 2x exy dx dy. 00 26 2x e Xy dx dy = | (Type an exact answer.)…

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Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3…

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Q: *csch(2 sin 2x)cx 1. V1-4x let u= du=

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Q: 6. Find all the values of z satisfying sinh z = = -j1.

A: What is Hyperbolic Function: The hyperbolic functions in mathematics are comparable to the…

Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

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Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

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Q: b) sin 3x 3 sin x – 4sin3 x [Hint: sin 3x sin(2x + x)] Prove

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Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: (3+ 7cos (x)) sin? (x) de 28. 29. sin° (9y) sec² (9y) dy / tan" (2) cos" (2) dz 30. [tan(2t) – sin°…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: sin 2t sin 5t 10 58s2+ 441 20 s4+58s2 +441 84 O Option 3 Optlon 4 O Option 2 O Nons of the cholcss…

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Q: rION 4. Find du/dt for the following: 35. u = tan-(xy) ;x = sin t;y = sect x-y 36. и 3D In ;x = sec…

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

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Q: (x²+y2 ) prove ne du + y ax -2 sin2u ( Euler's Rule) 5. If u = cot-1 that x ду x+y

A: We use the Euler's rule of partial differential in homogeneous function to solve this problem.

Q: Solve 3 tan(z) = V3 over the interval [0, 27)

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); U =

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Q: nd the definite intergral upper 1 lower 1/2 sin-1(x)/ square toot 1-x2 dx

A: Integrate ∫121sin-1x1-x2dx                          ......................(1) Put sin-1x=t…

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

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Q: 7. Evaluate t' sin(2t“) dt .

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Q: 1. L{sc" sin wt} L{e* (acost+6 sin t)} -kt cosh 2t +-sinh 2t 2 3. L 2.

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Q: Q.2 Find [(x' +5x² – 2) sin 2.xdx . c Inx

A: According to Bartleby Q&A answering guidelines I can answer only one question

Q: 25. æ sec (a²) tan(æ²) dæ | sin? x dx (Hint : cos (2x) 26. 1 27. dx 4- (ӕ — 1)? 1 dx 9x² + 25 28. dx…

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Q: GUESTION 3 dy Fmid Tx 2. 3.1 sinh e 3.2 %3D (Simiplify = Sech Cuox) answer fully your

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Q: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x)

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: 2. A. If : = sin(3x+2y) , verify that 2 -3 = -6z ax2 B. If f = x³y3 + 2xcosy + y?lnx then show that…

A: x=sin (3x+2y)

Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

A: z=2 cos x-sin xy ; x=1t; y=5t   see z is a function of x and y ,where x and y are functions of t so…

Q: dz Let z=sinh -(y-2x), where x = we and y=In then is given by du

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Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: sinh (1+Inx)= Select one: ex-1 2xe O Zero e Inx 2 O None e?x² +1 2xe x² +1 O 1+ 2x

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Q: 2. [ (1–3x)sin(}x)dx 4w dw 3. [* w°e™ dw w²e* -1

A: This question is taken from the definite integral in which we have to find the integral of the given…

Q: 1 Evaluate the equation /o x² sin (xy)dydx

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Q: y= 13.cos(5x) + sin (5x) 04 X6 2 COS 1.) Local Maximum poin to) are ? 2) Local Minimum. point(s) are

A: Maxima and minima occurs at dydx=0 We also check value of d2ydx2 to clarify that point is minima,…

Q: (f) If w=4x² +4y² +z² ,x= p sinø cos0, y= psinøsin0 , z =pcosø, Əw find and ap

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Q: 0.5 COS T - In(4 sin z) dz. J0.1

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Q: | 10(2 sin(x)) cos(x)dx if J Ax)dx = 13

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Q: x2 3 |5 – x + C а. 5 – x3 - cos t dt 1 + sin t In 1+ sin(t)|+C b.

A: Two integrals are given by, ∫x25-x3dx and ∫cost1+sintdt. The objective is to give the step by step…

Q: .4. (c) y = x*; y = sin(Tx/2); about x = -1

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