dx When the integral ex4- e2x is evaluated by trigonometric substitution, the integrand is transformed into? (a)금 cos? 0 (c) sin² e (b) sec² e (d) 는 csc? 0

Q: Q4:B/Simplify [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's theorem?

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Q: | sin(6y) sin(8y) dy.

A: we have to solve the integral

Q: a tan secy dy dx Jo Q2) a) Find b) Is cos4xv2 - sin4x dx = (2- sin4x) + C true or false? show me

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Q: What is the integrable form of sin-cos-sin0 d0? 2 2 A du B cosu du 2 -: / sinu du D du

A: Let's find.

Q: 3. Express 1+cos2x in terms of cos x. hence a. Evaluate (1 + cosx)dx b. Express 1- cos2x in terms of…

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Q: rĩ sec² 0 (e) tan 0 do. Vtan 0

A: That's easy. Have a great day!!!

Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: Prove a (cosa + cosß) + (sina + sinß) = 4cos² (@ - B) 2 %3D

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Q: d Prove that 1 da (sin-1æ) = V1 – a? -

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Q: 3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of…

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Q: What is the integrable form of sin-cos-sin0 d0? 2 A /1 – u² du B Vu²-1 du © : fcomndn cosu du D sinu…

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Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

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Q: 2 Find def differentiêt equatcn of: -I(082 Siny %3D

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Q: 1 Proof (I): (sinhx)' = Vx? +1

A: Given: The equation is sinh-1x'=1x2+1. To prove: The main aim is to prove the equation. Concept: The…

Q: E prove that = - Cotx + C %3D 1- Cosx +Sin'x

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Q: e in Q2, find Sin (2e) with 6 If csce -6,

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Q: 4 cos ' (sin (ax t)

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Q: Complete the integration: 1 1 Scos (2x)dx = sin 2x -sin 2x + C Determine the value of "?".

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Q: sin 20 d0 J Vcos² 0 + 16 V cos?

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: | cos (5x) cos (3x)dx

A: Given integral: ∫cos5xcos3xdx We know, cosαcosβ=12cosα+β+cosα-β. Also, ∫cosxdx=sinx+c.

Q: Assuming that |a| < 1, find the value of cosh ax dr. cosh x

A: It is given that,a&lt;1, we have to find the value of              ∫0∞coshaxcoshxdx

Q: tanla= 2 with 3T LaL2p 3 2 and Sin lb) = 3 with IT L6LT 2. %3D

A: Solution:-  tana=-23   with 3π2&lt;a&lt;2π (fourth quadrant) sinb=34 with    π2&lt;b&lt;π   (second…

Q: Y= 5-e- COSX by %3D

A: Given: y=5-e6y=cosx( This question is don't have to specify word  find  and how to find the answer)

Q: um point(s) for y=sin 2x- cos. d be in ovprossed in rodians

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Q: The integral O cose de 1-sine sec²0 de 1+ tan sece tane de sece - 1 S sine de 1+ cose x dx can be…

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Q: An appropriate trigonometric substitution 1 -dx is V4 – x² for x = 2 tan(8) for 0 E (-5,5) а. b. x =…

A: The given integral is: ∫14-x2dx

Q: Prove (Start either from the LHS or the RHS but DO NOT work from both sides at the same time) 1.…

A: sin2x=1-cos2x and,  tanx= sin(x)/cos(x)

Q: To evaluate f dx, the integrand can be transformed to 1-sin?x

A: Follow the procedure given below

Q: What is the integrable form of sin-cos-sino de? 2 (A -2 | sinu du B / Ju?- 1 du 2 /1-u² du D cosu du

A: Given: ∫sin θ2 cos θ2sin θ dθ Find the integral form of the given function. By using trigonometric…

Q: 2. Apply appropriate trigonometric substitution to compute the integral 1-4x +2 dx /2x

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Q: Consider sin °x cos2x dx. f we let 4=cos x, the integrand can be transformed to

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Q: Consider - Vx2-9 x3 dx. Using trigonometric substitution, what is the integral form in terms of 0?

A: To solve a certain type of complex integrals we usually simplify them using basic trigonometric…

Q: 1 Use the definition of the hyperbolic functions to prove the identity 1– - = tanh?(2x) cosh?(2x)

A: Explanation of the answer is as follows

Q: Find a series of cosines of multiples of x which will represent (x sinx ) in the interval (O, x) and…

A: Let's expand x cos(x ) , xcosx=x1-x22!+x44!-x66!+...=x-x32!+x54!-x76!+...             in 0,x To show…

Q: cosh(2æ) – 1 Verify the identity sinh? (x) using the definitions of the hyperbolic functions.

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Q: What is the integrable form of sin-cos-sine de? 2 2 (A) - - B -2 sinu du (D cosu du

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Q: The x2-4 dx can only be evaluated using trigonometric substitution technique. A True False

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Q: Find the product of the integral ri sec²(cos(x))dxdy sin-y

A: Given ∫01∫sin-1yπ2sec2cosxdxdy

Q: what is the integration of x^2/(9-x^2)^3/2 using trigonometric substitution

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Q: e). Prove that Sin3A+sinA 25in2A -COSA

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Q: What is the integrable form of sin-cos-sine de? 2 2 V1-u? du -2 sinu du u² – 1 du 2/ cosu du

A: We have given integral Let, I=∫sinθ2cosθ2sinθdθ As, sin2x=2sinxcosx sinx=2sinx2cosx2 So,…

Q: Find the trigonometric integral ∫sin2 x cos3 x dx

A: We have to find the trigonometric integral: ∫sin2 x cos3 x dx Rewriting the integral, ∫sin2 x cos3 x…

Q: Find this second derivative: dz O 2 cos a? – 4x² - sin x² O 4x² cos x² – 2 sin æ² O 82² (cos z²)…

A: Given : Second derivate of sinx2

Q: Find the trigonometric integral ∫sec4(x/2 ) dx

A: To evaluate the trigonometric integral , ∫sec4x2dx Solution: Put x2=t in the given integral we get,…

Q: Solve y' = y3 cos x (Show clear work!)

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Q: E prove that - Cotx + C 2 |- Cosx +Sinx

A: Solve the integration

Q: Find the area bounded by the trigonometric curves y=sinx and 2.828 square units 1.414 square units…

A: Given that curve y=sinx and y=cosx    from x=π4 to x=5π4To find :Area bounded by the region from…

Q: cos400 de J3- sin40

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Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

A: