a) Integrate the following expressions with respect to x. Then, find the value of the function integral when x equals to 1. ii. e* cos 2x dx

Q: I. Evaluate the following integrals. Check by differentiation. sin y dy cos²y

A: Given: ∫sinycos2ydy

Q: Approximate the following integrals using the Trapezoidal rule. 0.5 [h=24 dx x-4 a. [x² dx 10.5 b.

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Q: sin x dx

A: This is a problem of integration. Based on the general formula of integration we will solve the…

Q: Q2 - Evaluate the following integrals i. S cosx sin*x dx sinh³x -dx cosh®x

A: As per our guidelines we are only supposed to solve first question in case of multiple questions We…

Q: Use integration by parts to evaluate the following Integral S3 cos x? dx

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Q: Evaluate the integral. (Use C for the constant of integration.) sin?(x) cos (x) dx

A: The given integral is ∫sin2πxcos5πxdx. Let u=πx. Then dx=1πdu. Solve the given integral using the…

Q: Evaluate the following integral. Show and justify work ∫ cos(tanx)/cos2x dx

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Q: b. I = S(1+ sin x)5 cos x dx

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Q: (x² + 2x) cos(2x) dx

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Q: Evaluate the integral: |x cosh x² dx sinh x +C 2 x sinh x? +C sinh x? +C x² sinh 2x +C

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Q: I. Evaluate the following integrals. Check by differentiation. S sin 50 cos 50d0

A: Given;            ∫sin 5θ cos 5θ dθ Apply u-substitution: u=cos 5θ⇒du=-5 sin 5θ dθ            =∫-u5…

Q: 2. Use a substitution to change the integral into one found in the table of integrals, then…

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Q: I = S(1+ sin x)³ cos x dx

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Q: 15. (ez + e-z)2 dx.

A: Given: I=∫01ex+e-x2dx As we know from the hyperbolic trigonometric identities; 1). sinhx=ex-e-x2 2).…

Q: dx x Vx² +3 2

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Q: 1 x?g* dx. -1

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Q: Evaluate the following indefinite integrals using integration by trigonometric substitution.…

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: To evaluate the integral by making the given substitution

Q: tan(x)dx, Ind: u = cos(z)

A: We have to calculate the given integral: ∫tan x dx We know the identity, tan x=sin xcos x Therefore,…

Q: Evaluate the following by changing the order of integration: 5 sin(y*) dy dx. 5x

A: First we change the order of integration and find limit of integration.

Q: Q2 - Evaluate the following integrals i. S cosx sin*x dx

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Q: evaluate the following indefinite integrals using appropriate integration formula

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

Q: Evaluate the following integral by changing the order of integration. I | cos(x*) dx dy

A: We have to evaluate the integral by changing of order.…

Q: 1. a° cos(2)da = %3D

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Q: sin x cos? x dx

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Q: dx 16. 2 2 x*Vx –16

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Q: Evaluate the following integrals and check by differentiation: 1. J cos 4 x dx. 2. J 5 sec2 2x dx.…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: Evaluate the integral. (Use C for the constant of integration.) 4 sin Vx xp

A: To evaluate the given integral.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: Given,           ∫sin4(x)cos(x)dx   and use substitution u=sin(x)

Q: Use reduction formula to evaluate the given integral xe" dx

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Q: evaluate using Integration by Parts, substitution, or both if necessary.

A: Given integral is By using the following substitution, we get

Q: Using an appropriate substitution, the integral f e cos(e* + 1) dx is equal to:

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Q: (1 – 3|x|) dx -2

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: valuate the following integral using integration by parts x sin (1/7)x dx

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: We need to evaluate the following integral  I = ∫cos6xdx…

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫x cos-1 x dx

A: Given: I=∫xcos−1xdx

Q: f(cos*x- sin *xkx *a

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Q: ∫dx/(sinx)(cos2x)

A: Integration is calculated using basic properties.

Q: Evaluate the following integrals using Integration of Hyperbolic Functions. 14. S sech? ( Inx) dx…

A: Integration is the inverse of differentiation and we are going to use that concept here. Therefore…

Q: 16. | (ez/a – e-xla)dx. n/3 sec 0 tan 0 do. Vesec e 17.

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Q: 3n/4 cot a In(sin r) dx

A: Use integration by parts

Q: 1. sin Va +1 dx

A: The integral function is ∫sin3x+1dx

Q: Find approximate value of the following integral by using the trapezoidal rul 10 " 10 sin(20x²)dx…

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Q: 1 1 x=6 x - 2 dx +oo

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

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Q: Evaluate the following integral. x2 dx V1- 144x x2 dx = V1-144x? (Type an exact answer. Use…

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Q: Evaluate the integral. (Use C for the constant of integration.) cos a da sin a

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Q: 1. Evaluate the following integrals using integration by parts. In x | sin-y dy

A: "Since you have posted a question with multiple sub-parts, we will solve   the first three sub-parts…

Q: By reversing the order of integration, evaluate the following integral. To ²² x cos (y²) dy dx. co

A: The given problem is to evaluate the given double integral by reversing the order of integration.