Use the Fundamental Theorem of Calculus to evaluate os) dx a) sincos xp 0,

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Q: Evaluate the definite integral of the trigonometric function. U 6 + sin x) dx Need Help? Master It

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Q: Derive the De Moivre's Theorem with detail Explanation?

A: Statement: For any real number x, we have (cos x + i sin x)n= cos(nx)  i sin(nx) Or, (eiθ)n=eiθn…

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A: Here we have to prove, sinx·cosxtanx=cos2x

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A: Introduction: Laplace transformation and inverse Laplace transformation is very significant in…

Q: 5.3.24 Question Help 77T/4 y=sinx+cos x Evaluate the integral (sinx+ cos x) dx using the fundamental…

A: Given integral is,

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A: Given that  The integral  To determine the integral

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A: We have to prove cotz=coszsinz

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Q: Evaluate the following definite integralsusing the Fundamental Theorem of Calculus, Part 2.…

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

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A: We have to write the right side of trigonometric  identity.

Q: Quèstion 4 cosh (T-i) = e cosl + i e sin 1 e cos 1 + ie TI sin 1 2 e cosl - i e™ sin 1 + e cos 1 i e…

A: The solution is given as follows

Q: Find the area of the region that lies inside the curve r= 3cos0 and outside r= 1 + cos0. Show All…

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Q: vor use two and three Points 1 Gaussian Guadrature 2 (1+sinx) dx = I

A: Given integration is I=∫02πe1+sinxdx Let f(x)=e1+sinx Formula for two point method is…

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A: Given the curve  α:I⊂ℝ→ℝ4 given by t→αt=cost2, sint2, 2, αt

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Q: Cos t sed 2. (cos t) (cos t) sin(t) Cos t sin t cot t %3D

A: Conversion of cosecant to sine is, cosecθ=1sinθ Conversion of secant to cosecant is, secπ2-θ=cosecθ

Q: 154. Use the Fundamental Theorem of Calculus, Part 1, to find sin x d dx √1-t²dt.

A: Topic = Derivative

Q: Question: Discuss the Singulortdier and Poles of Zěsinz fr2)=

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Q: Determine whether the statement is True or False. Verify it. If æ = sec(0) then S 22-1 dx S (sec 0)…

A: Here we use some standard trigonometric identities. We know that,           1+tan²x = sec²x

Q: -1 1 dx 4 1 (2x+3)

A: We use substitution method to solve this integration

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Q: Now, evaluating / y(x² + y°)¯'dA, | y(x? + y²)¯'dA = -dA x² + y? r sin 0 -rdrde 5x sin Odrde sin…

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Q: cos o cos(x sin 0); p} = r(p) cos po CoS O %3D = cos ¢ sin (x sin o); p} = r(p) sin po %3D

A: We have to prove the following result Me-xcosϕcos(x sin ϕ);p = Γ(p) cos pϕMe-xcosϕsin(x sin ϕ);p =…

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A: y = sinx ---> y = 2 sinx,  The graph is stretched along y axis by a factor of 2   y = 2 sinx…

Q: 1. S cosxsin²x V1+sinx dx by algebraic substitution

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A: This question is taken from the trigonometry in which we have to prove the given trigonometry…

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A: Sometimes the value of the integration can not find easily then We can find the value of the…

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A: Definition used -                                  tant = sintcost, cot t=costsint…

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A: Given query is to transform using identity.

Q: help

A: see 2nd step.

Q: laplace(u(t-2)sin(t-2) )

A: laplace(u(t-2)sin(t-2) ) = e-2ss2+1

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A: Solution Using the formula 2sin(a)cos(b)=sin(a+b)+sin(a-b)

Q: sin' Acos e de. (b) cosA de. Aus. (a) 37/256. (b) 5T/8 Evaluate (a)

A: (a). We use Gamma function to evaluate the given integral. (b). We reduction formula of cos(x), to…

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A: Hey, since there are multiple questions posted, we will answer third question. If you want any other…

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A: Given query is to verify the identity.

Q: aw C. If w=f(x,y) and x=1. cose, y=1. sine. Prove that aw +1 (0)² = x² + ²

A: Using chain rule

Q: (4) Use diffential equations to prove the trig identity sin(r + a) = sin(r) cos(a) = sin(a) cos(x)…

A: Given: sin(x+a)+sin(x)cos(a)=sin(a)cos(x)

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A: We have to find the solution of the differential equation sin θ-2r cos2θ dr + r cos θ 2r sin θ+1 dθ…

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A: Please note that according to guidelines only first Q is solved. Please repost other questions.…

Q: a. Use the definition to calculate 2x – 3 dx using right endpoints x = a +kAr . b. Verify your…

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Q: 5. f (t)=-3t*e0.5t +3.8t²e²4+

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Q: dnd tie r(t) = (3 cos t,3 sin t,3t)

A: Given: r(t)=<3cost,3sint,3t> Unit tangent vector formula is    T(t)=r'(t)|r'(t)|

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