Find the indefinite integral. (Use C for the constant of integration.) S cos a sin adx cos + C 7 sin" 6 + C + C 6. cos + C

Q: Verify the value of the definite integral, where n is a positive integer.

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Q: Use the basic integration rules to find or evaluate the integral. (Use C for the constant of…

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Q: Evaluate the integral. (Use C for the constant of integration. sin (0) cos“(8) de

A: Given: ∫sin3(θ)cos4(θ)dθ

Q: 2. Find the following indefinite integrals. Use Substitution and/or Integration by Parts when needed…

A: a) Evaluate  ∫sinθcos4θdθ         ...(1) Simplification: Put cosθ=t⇒-sinθdθ=dt in (1)…

Q: Evaluate the integral: ∫6/[(x+a)(x+b)]dx for the cases where a=ba=b and where a≠b.a≠b. Note: For…

A: The integral, ∫6x+ax+bdx.

Q: QS-by using the double integration, find the area that lies inside the curve ra(l+cos e) and outside…

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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: Find the general indefinite integral. (Use C for the constant of integration.) (u + 6)(4u + 7) du

A: Answer of given question is following below

Q: x*dx Using trigonometric substitution technique, | the simplified integral after substitution is: x²…

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Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) 1…

A: We first try to complete the square. -x2-12x=-(x2+12x)=-(x2+12x+36-36)=-(x2+12x+36)-(-36)=-(x+6)2+36…

Q: a) Evaluate the following Integration by parts for definite integrals. i) So xe-s*dx ii) 12 Sin-'dx

A: The given integration is  I) ∫01xe-5xdx II) ∫032sin-1xdx

Q: Evaluate the integral. (Use C for the constant of integration.) sin (0) cos (0) de

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Q: Evaluate the integral. (Use C for the constant of integration.) sin3(0) cos“(0) de

A: Here,

Q: S'z sin(x) cos(x)dx

A: Let I=∫-π20sinxcosxdx

Q: Find the general indefinite integral. (Use C for the constant of integration.) / (u6 – 2u5 – u?. du

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Q: Find the general indefinite integral. (Use C for the constant of integration.) 2(1 + tan?(a)) da 2…

A: We will solve this problem in following steps

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. (Use C for the constant of integration.) 2 cos(6) cos (sin(6)) de

A: The power rule of integration states that ∫vndx=vn+1n+1.

Q: Find the trigonometric integral. (Use C for the constant of integration.) (cos(2?))(sin(?) +…

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Q: Q: Find the integral for the following functions: - sin(x). esec( x) 1) S cos (x) 2) S 3ln?(x) dx

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Q: Q: Find the integral for the following functions: - 4) S cosh2 (x). sinh?(x). dx

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Q: Find the indefinite integral. S(sin(x) cos³ æ)dx cos r +C 3 а. O b.- ote +C cos r 4 sin a d. + C 4…

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Q: dx/(cos(x)-1) what is the answer to this integral? Use C for constant.

A: Use simple integration formula.

Q: Evaluate the integral. (Use C for the constant of integration.) 9 sin?(t) cos“(t) dt

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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: valuate the integral. 10 sin?(x) cos3(x) dx CoS

A: Perform integration

Q: Find the indefinite integral. (Use C for the constant of integration.) 8 de cos(8) – 1 8 cot +C

A: The given integral,∫8cosθ-1dθ

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt cos?(t) V7 + tan(t)…

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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 indefinite integral: S 5e5" sin(e5) dæ

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Q: luate the integral. (Use C for the constant of integration sin(2x) xp 21 + cos?(x)

A: The integration of  sin(2x) / (21 + cos2(x)).

Q: b) f6xæ**dx 4 cosht)dt

A: We have to find the integrals.

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

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Q: Evaluate the integral. (Use C for the constant of integration.) e^−θ cos(3θ) dθ

A: ∫e-θcos3θdθ We need to Evaluate the integral Using C for the constant of integration.

Q: Use integration by parts to find the integrals shares e) f sin? @ de f) esint sin2t dt 8) x²e-* dx…

A: Evaluation of the Integrals

Q: Evaluate the integral. (Use C for the constant of integration.) 2 cos (a) da sin(a)

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Q: Evaluate the integral. (Use C for the constant of integration.) 5 cos?x sin 2x dx

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Q: Solve the following integrals: i. S(e**sin(2x))dx using integration by parts or tabular meth

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

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Q: Find the general indefinite integral. (Use C for the constant of integration.) (u + 9)(5u + 6) du

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Q: Find the general Indefinite Integral. (Use C for the constant of integration.) (u+7)(4u+9) du

A: Solve the following integral

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt cos?(t) V5 + tan(t)…

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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: aluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

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Q: the indefinite integral. (Use C for the constant of integration.) sin 50 cos 50 de

A: Apply substitution method

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt | cos?(t) V6 + tan(t)…

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Q: Evaluate the given integral as indicated: Use Integration by Trigonometric Substitution x³ dx 5 (4x²…

A: Given   ∫x3dx4x2+152 Use substitution as  4x2+112=sinθ to solve the given integral.

Q: x cos(4x + 1)dx

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Q: Evaluate the integral. (Use C for the constant of integration.) cos (@). 4 da V sin(a)

A: Here we evaluate the integral∫4 cos5(α)sin(α)dα

Q: Evaluate the integral. (Use C for the constant of integration.) e- cos(50) de

A: We have to evaluate the integral I=∫e-θcos 5θ dθ