Question Using trigonometric substitutions, fx'V4 + x*dx is equal to: O This option This option (4+ x)i - wa+x+c O This opton This option

Q: aw 1(dw If w = f (x,y) and x=r.cos0, y=r.sine Prove that - * = $² + fy² ar 2a0

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Q: cos /2rdt Hint: let 2t = u [Arc sin - xdx

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Q: 4 Using trigonometric substitutions, ſ xV16 dx is equal to: - x V16 – x2 + C /16 - x2 -In -4ln + C…

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Q: Evaluate using Trigonometric Substitution: dx (16+22)? z(z+24) 12+16 + 6 tan-14 + C O None of the…

A: We have to find Given Integral.

Q: Yandex Question If F (s) = then (s+1)?+4 f(t) = e-t cos(2t) - e-"sin (2t) f(t) = e³tsin (2t) %3D 1.…

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Q: 13. Given y = arcsin(x) – x/1-x² , what is y'? 2r? A) |1-. 2x B) C) D)

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Q: | 12sin z cos zý3 sin? z + e® dz

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Q: Show that if z = x+ iy, then: | cosh-z|2 sinh x Hint: use the equation: | coshzf = sinhx+ cos"y

A: We have , z = x + iy We know that ,  coshz = ez + e-z2 Therefore , cosh (-z) = e-z + e-(-z)2 = ez +…

Q: dx by using the trigonometric substitution of x 3D V12x? Find sino.

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Q: Given: In (sin² 3t) = e = arc cot (w) Find: dw dt O(1+w²) (6cot (36) e) [ Oet+w²et - 6tan (3t) - 6w²…

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Q: du du 1 If u = tan show that r + J: sin 2u. %3! ar X-y

A: To show the given expression using u.

Q: 3. Г dx (Hint: use a trigonometric substitution) 2 xVx2-1

A: In the part 3 we have the the value as ∫22dxxx2-1 . In order to make the substitution  we will…

Q: a. Y = cot(Ve“ ) tanh(e") -1 (sin(x²)) tan(2²) tan(ray) = x + y? b. y = C.

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Q: dx Using Trigonometric substitution, prove that J A-rž arc sin x + C

A: The given integration is ∫dx1-x2     . We have to solve the integration using Trigonometric…

Q: our trigonometric identities to hel +5} 2t) + 7 sin(2t)} (3,0<t<5 10,5≤t≤8 t≥ 8 .0 - 2y' + 5y = 10};…

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Q: 2) Use the quotient rule to prove the following. x=D1 [Please reference the Chapter 3.5 lecture…

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

Q: Evaluate and show all necessary solutions. 1.S cosxsin²x V1+sinx √25-4x² 2. S 3. S 4. fxcosxsinxdx…

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Q: 2. If P(x, y) is on the unit circle, then x? + y? = So for all i we have sin't + cost =

A: We Know that, In case of the unit circle: Radius r = 1 and  Standard form of circle passes through…

Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

Q: Using trigonometric substitutions, - dx , x > V3, is equal to:

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Q: Evaluate each of the following: 1. ſ cot 2v dv

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Evaluate using Trigonometric Substitution: 1 dx 1+yx O V1- Væ(v¤ – 2) + C V1+ va(V + 2) + C O V1+…

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Q: Which of the following is equivalent to -dx 1+ cosx – sinx after appropriate half-angle substitution…

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Q: s2 Q.3) Prove that L-1 () =(coshat sinat + sinhat cosat) 4+4a4, 2a

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Q: (g Suppose cos(a) = - and sin(a) is positive. 3 If the point (-2, y) is on the terminal side of the…

A: Given,           cosα=-23 and sinα is positive. Also, the point -2,y is on the terminal side of the…

Q: 10. Use an appropriate Trigonometric Substitution to integrate: 16 dx x2-8x+16 a) Jave Va-64 b) S-…

A: Integration problem

Q: 13. Evaluate using the substitution u = 1 – x² or trigonometric substitution. (b -ак х (a) dx x4 (c)…

A: Thank you for the question, As per our honor code we'll able to solve only first three sub parts of…

Q: Question with last attempt is displayed for your review only V10 with A in QIV and find 3 Let csc A…

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Q: Using trigonometric substitution to evaluate, 2 5² dy y√√y²-25

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Q: * What trigonometric substitution should be used to evaluate x² - 9 dx? x2 A x= 3tane B x= 3sine…

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Q: Fina the exalt val giren than sincu cos(v)=15 17 and Sincut!

A: We have to find

Q: Sinex dx is a) Conv. to o 6) diverge b) cont. to 프 auou (P

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Q: tor 7(t) = 2 costî+ 2 sin 2t ĵ + cos 2t k. %3D

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Q: 7. 10 Integrate the given belo trigonometric substitution by dx S Vix?+2x) O x +1 = sin 0 O x = sec…

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Q: 2х + 1 -dx. NOTE: In (M²) = Pln M х? + 1

A: To determine:

Q: When integrating by trigonometric substitution | V4x² +25 dx becomes a) jsc 25 sec? O tan O dO 2…

A: Solve

Q: %3D 20 24 tan 24 through solve this egni: Hint :oU=KL +2 =0 மு 3K²=Par ET %3D 2.

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Q: 1. Use a Trigonometric substitution to evaluate the following: Vy² – 25 -dy,y > 5 y Include a sketch…

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Q: X sin²= cos7 zcos'dx ·COS 2

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Q: cot a In(sin r) dr "/2

A: We know that integration of xn is xn+1/n+1. We know that : cosx/sinx= cotx.   Here i attached…

Q: Using trigonometric substitutions, xv16 4 dx is equal to: V16-x -In O This option Ths option 16 In…

A: Take substitution of x = 4sin(theta).

Q: 1. Use Trigonometric substitution to evaluate f dx. Hint: Ju? – a² let u a sece.

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Q: Using trigonometric substitution, what is S Vx-9 dx ?

A: Given that                                                   I=∫x2-9x3dx let…

Q: 2. Using trigonometric substitution, what is S x² -9 dx ? x3

A: Given integral √x^2-9 /x^3 dx

Q: The appropriate trigonometric substitution for dx is V3x-x2 ww 3 X = 9 3 + sec 0 2 4 3 +sine x = O…

A: We have to solve

Q: 213 If cot 0+ tan = and sece - sece = y, Prove that (x'y)° (xy²)*° = %3D

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Q: (1+cot 0) de 5. sin e4 - cote

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Q: S sec²0 do 1+tano seco tane de seco - 1 The integral O 1: S S x dx x²+√√√x²-1-1 coso do 1-sino sino…

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Q: Using trigonometric substitutions, dx, x > 3, is equal to:

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Q: 4) Sin W = %3D Cos N = W. Tan W = %3D

A: Solution: The objective is to find the required values

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.