Exercises 57–62 require the use of various trigonometric identities before you evaluate the integrals. sin² 0 cos 30 d0 os² 20 sin 0 dð 58. 57. | sin 0 cos 20 do os³ 0 sin 20 d0 59. 60. 61. sin 0 cos 0 cos 30 d0 62. sin 0 sin 20 sin 30 do

Q: Evaluate the integral. T/3 2 sin(8) + 2 sin(8) tan2(0) sec2(8) de

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Q: Evaluate the integral. ∫Sin3 θ Cos 4θ  dθ

A: We have given;

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A: To evaluate ∫0π2 sin4x . cos3x dx using WALLIS formula.

Q: Prove that: 1-tan? 0 cos? 0 - sin? e %3D 1+tan? 0

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A: Let and differentiate it with respect to and find .

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A: To Determine: find the integration  Given: we have ∫x cosx sinx dx Explanation: we have ∫x cosx sinx…

Q: Evaluate the integral. π/2 sin³ 0 cos²0 de 3

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Q: In Exercises 17-26, use an addition or subtraction formula to find the exact value. 17. sin- 12 18.…

A: Given 1)sin(7π12) 2) cos(105)We need to find the value using addition or subtraction formula

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: Evaluate sin (; - i In v2) cos(; - i In i ln v2) i In /2) cos o (3/4)i o (3/8)i o 5/8 o 5/4

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Q: Find or evaluate the integral

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A: The cosh x and sinh x are given by, LHS =

Q: Evaluate the integral. 8 sin(0) + 8 sin(0) tan²(0) de sec?(0) • 57/3

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Q: Evaluate the integral. sin COs 503 502 502 sin 50 1. cos d0 3D 502 502

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Q: sin 50 do 1+ cos 50 Evaluate the integral using the substitution u = 1+ cos 50. sin 50 do 1+ cos 50…

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Q: Evaluate the integral. "a/3 6 sin(0) + 6 sin(0) tan2(0) do sec?(0)

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Q: Evaluate the integral. 1 信 sin COS do 20² 20² 1 作素图 sin COS de = |0 | 20² 20²

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Q: Evaluate the integral | : sin 20 do 3+ cos 20 using the substitution u = 3+ cos 20. sin 20 Op 3+ cos…

A: In this question, we need to evaluate the integral ∫sin 2?3+cos 2?d? using the substitution…

Q: Evaluate the integral.

A: We have to evaluate ∫3sinθ cosθ dθ Let substitute t=sinθ ⇒dtdθ=cosθ⇒dt=cosθ dθ Substituting the…

Q: sin 40 Evaluate the integral : do 3 + cos 40 using the substitution u = 3+ cos 40. sin 40 do = 3+…

A: Solve by substitution method

Q: Evaluate the integral. 6 sin 0 + 6 sin 0 tan² ® sec2 0 a/3 de

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Q: Solve the integral of 2sin(x)/(1+cos^2(x)

A: We have to solve the integral.

Q: Exercise 3. Show that (a) sin z = sin z: (b) cos z = cos 7.

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Q: Another form of sec x dx cos x 1- sin²x b. Use the identity in part (a) to verify that 1. |1 + sin…

A: a) we have to verify the identity sec(x)=cos(x)1-sin2(x)Consider, RHS=cos(x)1-sin2(x)we…

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Q: 18. Find three integrals in Exercises 39–74 that can be solvedby using a trigonometric substitution…

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Q: Evaluate the integral : sin 60 do 2+ cos 60 using the substitution u = 2+ cos 60. sin 60 do = +C 2+…

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Q: Evaluate the definite integral: 2, 1 sin 0 + cos 0 +1

A: Given that: ∫0π21sinθ+cosθ+1dθ

Q: Show that given that z = sin-12 дхду дудх

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Q: Evaluate the integral ∫cos√θ/ √θ sin2 √θ dθ

A: We have to evaluate the integral: ∫cosθθ sin 2θdθ We know the trigonometric identity, sin 2A=2sin A…

Q: Solve 2 sin (z) – sin(z) = 1 over the interval (0, 2) O z= O z= 5, O z= ,, 2'6

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Q: (4) |sin² 0 cos0 d0

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Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: What is the integrable form of sin (0) do? sin cos

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

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Q: Verify the identity. 2 cs" e 1-- 1+ sin 0 = sin 0

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Q: sin 70 do 9+ cos 70 Evaluate the integral ; using the substitution u = 9 + cos 70. sin 70 do 9+ cos…

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Q: Evaluate the integral / sin 50 do 2+ cos 50 using the substitution u = 2+ cos 50. sin 50 do 2+ cos…

A: Recall: ∫1xdx=ln(x)+C

Q: what is the integral of cos(6x)xsin(sin(6x)) from 0 to pi/12

A: Given,

Q: Evaluate the integral. 6 sin (2x) In ( sin (2x))dx 6 sin (2x) In (sin (2x))dx = (Type an exact…

A: Please see the explanation below.

Q: Evaluate the integral. sec 0(sin 0 cos 0 + cos 0) de Jo

A: Let I=∫0π/2secθsinθcosθ+cosθdθ

Q: Using Wallis formula, find the integral of the expression. Answer in 5 decimal places (example…

A: We have to solve given integration with the help of wallis formula.

Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

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Q: sin 80 do Evaluate the integral 7+ cos 80 using the substitution u = 7+ cos 80. sin 80 do 7+ cos 80…

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Q: Give the exact value of 37 sin(- 00 O undefined 1 O V2 2 2 V3 O-1

A: Here I am attaching image so that you understand each and every step.

Q: In Exercises 29-76, evaluate the indefinite integral.

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Q: [sin’ @ cos' Ode

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