2. Evaluate the following using trigonometric substitution. Show all necessary solutions. 2/2 dx (c) :::

Q: Evaluate the following using trigonometric substitution: dx V25 + x²)

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Q: V2 2. 2.

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Q: 1. Evaluate √2 √4x² dx using a trigonometric substitution.

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Q: Given that sin t = 1/2 and 0 ≤ t < π/ 2, find the value of cos t using a trigonometric identity.

A: Given

Q: Evaluate dx 1²√√²-49) SV x>7, using a trigonometric substitution.

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Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify…

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Q: In solving for the antiderivative of f(x)= (9 – x2)3/2 using trigonometric substitution, Jf(x)dx is…

A: Whenever we have a2-x2 , then substitute x=asinθ or acosθ.

Q: The integral [₁ face 8 dx S can be transformed to which of the following when trigonometric…

A: We have to solve above integral

Q: If sin t = 2√7/7, 0 ≤ t <π/2, use identities to find the remaining trigonometric functions.

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Q: Using trigonometric substitutions, S –a dx is equal to: xv16 – x²

A: Using trigonometric substitution to evaluate this integral as follows.

Q: 4 Using trigonometric substitutions, S dx is equal to: xV16 – x²

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Q: 1. Use trigonometric substitution to evaluate each of the following. (») /: dx x² + 4x + 3 (b) dx (4…

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Q: sin' x dx

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Q: Given that O 1800, determine the numerical value of this %3D sine = %3D -1 1

A: Put  thetha=180°

Q: L(sin?t +cos?t) is:

A: We have to find out Laplace transform of L(sin2t+cos2t). We know that (sin2t+cos2t) = 1

Q: Given that z = 4 ( cos· 4 +i sin) and w = 1 – iv3. Find 4. %3D a) 2 w b) E c) arg (-), in radians as…

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: Given that sin t =1/2and 0 ≤ t <π/2, find the value of cos t using a trigonometric identity.

A: sin t =12and0≤t≤π2i.e first quadrantIn 1st quadrant sin t, cos t arepositive

Q: Use the given substitution to express the given radical expression as a trigonometric function…

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Q: dx If x2 - 2x – 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: Evaluate the following using trigonometric substitution: dx Vx2 + 2x – 15

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Q: If u(t) = (sin(7t), cos(7t), t) and v(t) = (t, cos(7t), sin(7t)), use Formula 5 of this theorem to…

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Q: 3 + In?x dx

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Q: 4. Use the diagram below to complete the table. y B 4 Coordinates of B sin 4 cos 4 3n tan 4

A: We have to find coordinates

Q: dx If x2 – 2x – 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: After choosing the appropplate trigonometric substitution the integral 4x? dx, becomes 4 cos (0)de…

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Q: 3. Solve the following trigononetric equation for a. sin r = cos" r on [0, 27).

A: Given equation is: sin2x = cos2x                  on [0, 2π]

Q: Use this reduction formula and your answer in part a) to find ſ cosª xdx and ſ cos® xdx.

A: To find ∫ cos4 x dx and ∫ cos6 xdx First we find ∫ cos4 x dx Apply integration reduction…

Q: Solve the following equation? 2 Sin t Cos メ- Cos? メ-|, 2 where x E [, 2)

A: We can solve the equation for the value of x as below

Q: dx can be transformed to which of the following when trigonometric substitution is used? (x²+4)²…

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Q: Using appropriate trigonometric substitution, dx XV9 — х2 is transformed to

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Q: Use the trigonometric function f(t) cos (t + + 2 to answer the following questions.

A: Given:- f(t)=-cos(t+π/9)+2 To find:- phase shift of given trigonometry function

Q: Express the following as a function of a positive acute angle: cos 242°

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Q: Evaluate the following using the TRIGONOMETRIC SUBSTITUTION METHOD: 1.5 dx

A: Given: I=∫dxx2x2+4 For evaluating given integral, we substitute x=2tanθ…

Q: b) Solve the following trigonometric equations for 0° sx< 360°. (i) 2sec?x = 1 + 3tanx (ii) sin 2x…

A: Solution:Given(i) 2 sec2x=1+3 tan x(ii) sin 2x=cot xFormula:sec2 x=1+tan2 xsin 2x =2 sin x cos xcot…

Q: | (3x (За? — sin x + 2) dx

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Q: S= dx 3+ sinx+cos X

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Q: dx after appropriate use of trigonometric substitution, it will be transformed into? Vx² –4x+1'

A: Given That: The integration, ∫dxx2-4x+1

Q: 3) Solve the following for the angle 0 using CAST Rule, where 0 ≤ 0 ≤ 360 a) sine === b) cost = -√3…

A: Given that, a) sin θ = -12 b) cos θ = -32 By using CAST rule, find the angle θ. CAST Rule: If the…

Q: Using trigonometric substitutions, S xv16 - 16 dx is equal to: - x2

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Consider the following trigonometric substitution problem: dx Vx2 + 36 Making the substitution: x =…

A: The given integral is ∫xx2+36dx. Substitute x=6tanθ  and  dx=6sec2θ in the above integral and…

Q: Solve the following equation shown.

A: sin2u=15,  0≤u≤π2

Q: Evaluate the following using trigonometric substitution: Vx2 - 4 dx

A: Find your answer below

Q: 51. Compute x² _ and then using the identity dx in two ways and verify that the answers agree: first…

A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

Q: the Following Solve Sin x (Co Sk) y = t anx %3D

A: Divide whole equation by sinx in order to make dy/dx alone

Q: dx If x2 - 2x - 4 is solved by trigonometric substitution, which of the following substitutions is…

A:

Q: 3.) S(1 – sin²xcos²x)²dx

A: As per our guidelines we need to solve only one question. Please repost the remaining questions as…

Q: 3) Solve the following for the angle 0 using CAST Rule, where 0 ≤ 0 ≤ 360 a) sine === √√3 b) cose =…

A: a) sinθ=-12 By CAST rule, sinθ is negative in 3rd and 4th quadrant, So here 180≤θ≤360. Since period…

Q: Using a suitable trigonometric substitution, the integral dx 3 (16x² + 9)² is equal to sin 8+ C₁-<<…

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Q: dx 9. 3/2 (4-x2)³/2

A: Given:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.