√√2x-x² 7. Express the integral [²√√√²* A. B. C. D. E. •2π cos [²* " ["zrdz dr de = 1/2 fzr dz dr de -π/2 r2π 1²7 1² 2 cos 0 6²³. SV* z dz dr de rπ/2 -2 cos 0 [5/² √²8 zrdz dr de r -2πT L² fzr dz dr do Ꮑ /x²+y² z dz dy dx in cylindrical coordinates.

Q: 3. The integral of sin24x cos4x dx is a. (1/4) sin³ 4x + C b. (1/3) sin³ 4x +C c. (1/12) sin³ 4x+ C…

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Q: Evaluate the indefinite integral S- dx 3x² x³√x6-1 O 3+C sec-1 +6 O sec-1x3 3 + C ec²¹x² + C sec 3…

A: SOLUTION-

Q: press cos x √3sina in the form of Asin(x − a) with 0 < a <

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Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

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Q: 3) Evaluate ex*+¹sin (√x) dx].

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Q: 3. Compute : exp(sin m(e÷)).

A:

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: Evaluate f 3xV1 – 2x² dx A(1 – 2x*) + C B. (1 – 2x*) +c (1-2x²)³ D. +C 2 Evaluate S dx csc 2x-cot 2x…

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Q: One approach to evaluating 2 cos (2x)dx is to first rewrite it as cos(4x) + 1 dx а. cos(2x) – 1 dx…

A: This is the question of integration.

Q: 17. Use the theory of residue to evaluate the following definite integrals r2 (a) /" (b) / do 2+ cos…

A: 17(b) ∫02πcos2θ dθ5-4cosθ=real part of ∫02πei3θ dθ5-4cosθcosθ=real part of eiθsinθ=imaginary part of…

Q: Solve for x, x in [0, 2Tt). 4 sin 2 x - 4 sin x + 1 = 0

A: Given: 4 sin2x-4 sin x +1=0 , x in [0,2π).          (i) To find: x

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

A: Evaluate the integral by using substitution method

Q: Find the indefinite integral 3 cos 0(5 tan 0 + 9 sec 0) de. 0(5 tan 0+9 sec 0) d0 = (5t 3 cos 3 cos

A: we know that  tanx=sinxcosxsecx=1cosx

Q: /2 1. (a) Use the Wallis cosine formula to evaluate cos' x dx. (b) Evaluate | 1 - dx by using…

A: Wallis's formula state that 1. if  n is odd and n≥3,then ∫0π2cosnxdx=23.45.67 . . . n-1n Therefore,…

Q: The definite integral sin24x cos2x dx is equivalent to x/2 (A -sin²0 cos²0 d0 2 x/2 В 2sin20 cos40…

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Q: 3) fe-2x sin 2x dx 4) J√1 + cos 4x dx

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Q: Evaluate the definite integral 8 | (18a? – 8x + 3) da

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Q: (a/3 d(cosx) =? 24 - sinx O A) V3/2 O B) 1/2 C) -1/2 O D) -1/3 E) T/3

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Q: Solve the following ODE * (y sin x + xy cos x) dx + (x sin x+ 1) dy =0 1 Add file

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Q: Evaluate the triple integral 1 V1-y V4-z? y? COS cos (z? + y? + z?) dzdzdy. V12 + y? + z2

A: Given triple integral is ∫-11∫01-yz∫04-x2-y2cosx2+y2+z2x2+y2+z2dzdxdy To evaluate the integral.

Q: (5е? + 9* — 8 sin x)dx - 8 sin æ) de O 5e* + x° – 8 cosx + c x° - 8 cos x + c О Бе + x —— 8 sin x +…

A: Solving the problem by doing the integration.

Q: Compute the definite integral T/4 0 5 sin² (3x) dx

A: Sol:- ∫0π45sin23xdxTake the constant out:  ∫a·fxdx=a·∫fxdx=5·∫0π4sin23xdx=5·∫0π4121-cos6xdxTake the…

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: de a+bcose' where a> bl. Hence or otherwise evaluate 2n de √√2-cose 3

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Q: √ (3(1 + cos 0))² + (−3 sin 0)² do

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Q: Evaluate thne integrat -6 to -10. A. 21/2 B. 1/2 C. In 3

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: Evaluate the integral s sin³ (3x) cos³ (3x) dx . Osin¹ (3x) sin (3x) + C 12 18 -

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Q: Evaluate the Integral dx |. 1 + 2 ax X² 2

A: Consider the integration."Note that as per the rules, we are supposed to answer the first question…

Q: Evaluate i) A (x +e* + 2) _ii) A sinh (a + bx) iii) A cosh (a + bx).

A: