Find the integral a 3x? cos (x ) dx where a is some positive real number.

Q: Find the integral of ([sin(x)]^6)([cos(x)]^7)dx from x=0 to x = pi/2. a. 14/1001 b. 15/2002 16/3003…

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Q: Find the integral. cos xsin x dx

A: Given, ∫cos3x sin2x dx   We have to find the integral value

Q: . Find the integral [cos (3x - 2)dx

A: A detailed solution is given below.

Q: The resulting integral of sin-cos-sin0 de 2 2 has the form -F(0) - +C. What should be the value of e…

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Q: Evaluate the integral [e2 cos(2x)dx.

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Q: Compute the following integrals: sin x dx -T/2 :/3 |(cos x)(sin? x) dx -n/3

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Q: 2 X COS x dx ах

A: To integrate: ∫0π2x cos (x) dx

Q: 2n do 3 + sin 0 + cos 0

A: Given integral is ∫02πdθ3+sinθ+cosθ Given z=eiθ We know that  eiθ=cosθ+isinθ e-iθ=cosθ-isinθ So…

Q: Evaluate the given integral. ∫ (x cos x + x sin x) dx.

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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: Evaluate the integral from 0 to pi: ∫cos4(2t)dt

A: ∫0πcos42t dt

Q: What is the integral of sin? r cos x dx?

A: Given,           ∫sin2xcos2xdx

Q: S cos 2x dx

A:

Q: Evaluate the integral. x2 cos(7 x) dx +C

A: The given integral is: I=∫x2 cos(7x) dx

Q: 2 x cOs x dx.

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Q: Evaluate the integral. cos(5 x) dx

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Q: sin2(0) cos(0) d0, sin(0)

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Q: use the method for odd powers to evaluate the integral.

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Q: Evaluate the integral. (Use C for the constant of integration.) ∫ e4θ sin(5θ) dθ

A: we have to find the value of integral ∫e4θsin(5θ)dθ to find the value we use the formula ILATE which…

Q: evaluate the integral.

A: To evaluate the given integral.

Q: Obtain a formula that expresses the integral [cos". cos" x dx

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Q: evaluate the given integral.

A: To evaluate the given integral

Q: Find the integral. e4X cos 3x dx + C

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Q: Evaluate the integral. cos 2x dx

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Q: Evaluate the integral. ∫0 π Cos 6θ dθ

A: Consider the following integral: ∫0πcos6θdθ Consider the following equation: I=∫cos6θdθ Consider the…

Q: 0. sin? x cos? x dx

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Q: The integral of the function cos² x. sin a dx is

A: the given expression is: ∫cos2x.sinxdx

Q: тх e COs nx dx

A: We have to evaluate the integral  ∫emx cos nx dx.

Q: Find the integral of ([sin(x)]^6){[cos(x)]^7)dx from x=0 to x = pi/2. 14/1001 15/2002 16/3003…

A: …

Q: Use the value of the first integral I to evaluate the two given integrals.

A: It is given that, I=∫0π/2cosθ-2sinθdθ=-1 Consider the integral ∫0π/22sinθ-cosθdθ

Q: Evaluate the integral + 2x) cos x dx

A: The given integral is ∫x2+2x cosx dx

Q: Evaluate the integral cos (x) sin(x) dx using the substitution u = = cos(x). | cos" (x) sin(x) dx 13…

A: topic - integration

Q: Evaluate the integral Se cos(2x)dx

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Q: Evaluate the integral. cos x dx

A: We have to evaluate the integral.

Q: Find the indefinite integral.∫(cos5 t/√sin t)  dt

A: Given information: The indefinite integral is ∫cos5tsintdt Trigonometric identities used:…

Q: Evaluate the integral: a cos (4) dx x² sin² ( ÷) where a is a nonzero constant.

A: Given,  ∫  a cosaxx2 sin2axdx

Q: evalutate the integral from 0 to pi/6 sin^3(x)/cos(x) dx

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Q: a) Evaluate the integrals using appropriate substitutions. dx Sine i) S ii) S de Cos? 0+1 1+16x?

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

Q: Compute the indefinite integral. - sin z dx COS X Answer: + C

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Q: Evaluate the integral. (Use C for the constant of integration.) cos 30 de

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Q: d) S cos³x sin*x dx

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Q: Evaluate the integral. (Use C for the constant of integration.) e-0 cos 80 d0

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Q: Evaluate the integral. cos-1(x) d.

A: We have to evaluate I=∫cos-1(x)dx

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

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Q: Evaluate the integral COS° x dx

A: the given function can be integrated directly  it need to be converted into integrable form

Q: Find the indefinite integral. cos t dt sin t

A: Consider the given indefinite integral, ∫cos5tsin tdt use the trigonometric identity, cos2x=1-sin2x…

Q: Evaluate the integral cos (x) sin(x) dx 13 using the substitution u = cos(x). cos(x) sin(x) d.x ,13…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Evaluate the integral.

A: we have to evaluate the integral ∫excos(ex)dx

Q: Evaluate the integral.  integral cos  - 4  x  dx

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Q: Evaluate the integral cos (Ty) dy dr. dx.

A: