Evaluate using trigonometric substitution. (Use symbolic notation and fractions where ne dx 2 (25x2 + 4)

Q: If sin a = 3. find: a) csc a b) a

A: sinα=12 a). cscα=1sinα=112=2

Q: dy 2.

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

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Q: 2. sin 2wcos 2wdw

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Q: 1 cosxsec?x = %D COSX

A: To show the given Identity, just I have to go from one side and show the other side .

Q: 6. cos( 8.

A: (6)Given the trigonometric ratiocos(7π8)

Q: L{e-to , 3+} sin

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Q: cos?(t) COS 1-cos2 (t)

A: We have to simplify

Q: Evaluate 2 [²4x² - 4x³ - 2x + cos(x) dx. Note: If the answer is not an integer, round your answer to…

A: We need to evaluate the value of the following integral ∫024x3-2x+cosxdx

Q: Rewrite the expression so that it is not in fractional form. There is more than one correct form of…

A:

Q: Evaluate the followng- (メー2メ+3) dx ー2 Cos (70+5) dO

A: Formula used: 1)∫xn dx=xn+1n+1+C and 2) ∫cosx dx=sinx+C, where C is integrating constant. Given: 1)…

Q: Incorrect Your answer is incorrect. Rewrite sin 2cos as an algebraic expression in u. 4 :) - sin 2…

A: We use Trigonometry identities  Sin(2A) = 2 sin(A) cos(A)

Q: S2 Sinx

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Q: Evaluate the integral. /2 7 cos?(8) de

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Q: Evaluate ∫ sin(7θ + 5) dθ.

A: Let u=7θ+5 . Now differentiate this equation with respect to θ and solve for dθ . Use the power rule…

Q: Establish the identity. e(1- sin? 0) = 1 sec Rewrite the left side expression by expanding the…

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Q: 1 dr r/1+ x6 (use trigonometric substitution) 3.

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Q: II a.5 cos? =D5

A: You asked multiple questions but as per guideline I can do only one question. Please repost the…

Q: 102 /sin?xcos (2x)dx

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Q: lim, o (cos z)= takes which indeterminate form? А. 100 В. 00 С. оо D. Е. 1 х о 8 -18

A: Here, we can solve it by taking the limit of individual terms.

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

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Q: Evaluate p* sin 0 de dr.

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Q: 3 + In?x dx

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Q: "풍 2 secx dx tan³x + 4 tanx

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Q: Use de Moivre's Theorem to find the following. Write your answer in standard form. (−2√3+2i)4

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Q: dx x² +4x+29 3.

A: Explanation of the answer is as follows

Q: de 4TV3 Show that (2+cos8) 9

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Q: xp 2sin x+ cosX 3. Determine:

A: Indefinite integration

Q: ind the value of 2 (x+5) = 3(2-5x %3D

A: Given: 2(x+5)=3(2-5x)

Q: Fid2 fr fue= 5in°(え+22ーリ = Sin

A: Given, fx = sin6x3+2x-1   We have to find the dydx

Q: sin(48) cos(48x) dæ : О576 O -2 O 2

A: We have to find the value of definite integral

Q: 62 = c²+ a²-ca 6. Use the law of cosines to show that, ifb= 60°

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Q: (3) I= √(1-x²) ³² 203 x dx

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Q: ☺ Inpolar form, evaluate; 2(3+4i). 3(-344i)

A: .

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

A:

Q: 5. [ sinxcos^xdx

A: Use necessary identities.

Q: duce the following expression to a single trigonometi sec2 (x) tan(x)

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Q: 3. Evaluate the following using trigonometric substitution. Show all necessary solutions. dr (e) [*.…

A: To evaluate-  the given integral.

Q: Find |xV9x? +1 dx by using the trigonometric substitution of 3x = tan 0.

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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) cotx C) O 1-COS2X |-COSZX 2. cos?x

A: We have to simplify the expressions using identity: b)  cot xcosec xc)  1-cos 2xcos2 x We know the…

Q: 3. Rewrite the following in algebraic form – NO TRIG TERMS. Sec [arctan (x/4)]

A: The given trigonometric function is: Secarctanx4  This can also be written as: Sec-1tanx4

Q: 1 de (trigonometric substitution) x³Vx? -1 3.

A: We will use the substitution : x = sec(θ) and then proceed as follows :

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

A: Find your answer below

Q: 49. 8- 2r - x dr

A:

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

A:

Q: Prove the identity Sin3A=3SinA-4Sin3A

A: Given identity is,Sin3A=3SinA-4Sin3A

Q: dx 9. 3/2 (4-x2)³/2

A: Given: