Integral of cos2x on [0, infinity]

Q: Evaluate the indefinite integral S- dx 3x² x³√x6-1 O 3+C sec-1 +6 O sec-1x3 3 + C ec²¹x² + C sec 3…

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Q: Evaluate the indefinite integral ds= %3D

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Q: Use a double integral to find the area of the shaded region.

A: The formula for the area of a region of a polar curve, r(θ) bounded by θ=a to θ=b in the polar…

Q: 3 x2 - x dx 1

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Q: Show that 2x° dx = [; 2r° dx + f zr* dx + [,2x° dx %3D

A: Given that,    ∫142x2dx=∫122x2dx+∫232x2dx+∫342x2dx

Q: ind the indefinite integral using the formulas from Theorem 5.25. (Use C for the constant of in 5 dx…

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Q: dx Use the Substitution Formula to evaluate the integral x(Inx)*

A: The given Integral is ∫24dxxlnx2

Q: Determine the following indefinite integral. Check your work by differentiation. 3 dt 64t + 64

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Q: Show that arctan(Tx) – arctan(x) -dx In T. by first expressing the integral as an iterated integral.

A: To show

Q: a) Evaluate the indefinite integrals using Repeated Integration by parts i) fx²e-2*dx ii) fx?Sinxdx

A: We have to evaluate the given integration.

Q: a) Evaluate the indefinite integrals using Tabular Integration by parts. i) (x² + x + 1)Sinxdx ii)…

A: Given: I1=∫x2+x+1sinxdx, I2=∫x32x+1dx For evaluating I1, we will use integral by parts theorem…

Q: a) Evaluate the indefinite integrals using Tabular Integration by parts. i) ſx³ V2x + 1dx

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Q: A definite integral Evaluate In x dx.

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Q: sec² 0 de. 1- tan 0 Evaluate the improper integral:

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Q: cos (n/x) dx Cos x2

A: Given: ∫cosπxx2dx

Q: Сompute L f dx, where f(x)=|x|.

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Q: (c) / cos(3t) + sin(5t) dt (f) (tanr+cot r) dr

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Q: Determine the following indefinite integral. Check your work by differentiation. 7 4 2 dx x2 4 +2 dx…

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Q: use a double integral to find the area of the shaded region.

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Q: -1 dx 3 x² -4

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Q: Find the indefinite integral by making the substitution x = 2sin(theta)   integral of…

A: Given integral:∫x(4-x2)32dxwe need to evaluate the integral by substituting,x = 2 sinθ

Q: Use the substitution u = 3x²-2 to find the following indefinite integral. Check your answer by…

A: We need to find integral.

Q: Prove that X+1 Cothx=-In

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Q: Write a definite integral which computes the area of a surface of revolution 3 1 from rotating y=-x²…

A: Topic- Application of Integration

Q: Determine the following indefinite integral. Check your work by differentiation. (5+4 cos y dy sin?y…

A: The given integral is ∫5+4cosysin2ydy. ∫5+4cosysin2ydy=∫5sin2ydy+∫4cosysin2ydy=5∫cosec2y…

Q: Compute this improper integral showing all steps.  integral of x ln(x) dx from 0 to 2.

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Q: S Prove that £{cos(at)} = est cos(at)dt s² + a² integrating by parts twice and the evaluation of the…

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Q: Determine the following indefinite integral. Check your work by differentiation.

A: Evaluate the integral.…

Q: Determine the indefinite integral. Check your work by differentiation. dx O A. 5 In |x| + 3x +c 20 +…

A: Evaluate: ∫5+x3x dx

Q: dx: Evaluate the improper integral if it exists The improper integral diverge:

A: ∫1∞1x3dx=-1x2

Q: 5+ 2x dx x(3x² – 4)5 dx

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Q: 10) evaluate the integral (Usec for theconstant integration e- cos (ro)de

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Q: Evaluate the integral -21 cos(-2t) dt Note: Use an upper-case "C" for the constant of integration.

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Q: f(x) = 1- r, 2 V

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Q: 1 - dx x In x 2. Evaluate the improper integral or show that it is divergent.

A: To show that it is divergent.

Q: (e) / 3. (c) (Зх — 5)3 dx (d) / ((V– 5)² – x)² c - -

A: (c)

Q: Evaluate the indefinite integral. | 2* (2° + 1)/2 dx Integral =

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Q: Evaluate the double integral of the function over the rectangle cos(2x) sin(y) dA, R = 0, 0, 2.

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Q: 5) Evaluate ehe integral (use c fos Ane constant of integration. tan'cx)cos x) dx

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Q: (a) /(3=² (За? — 6х + 5) dx - 1 .5 x° + 5 1 (b) dx - 4

A: To determine the value of definite integrals.

Q: Evaluate the definite integral using the Fundamental Theorem of Calculus. 64 (1 Vx)2 dx 16 2x

A: we need to evaluate ∫16641 - x22x   using fundamental theorem of calculus if F(x) be any…

Q: definiuon of the integral given in Theorem 4 to evaluate the integral. | (x +2x-5kdx Hint: > n(n+1)…

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Q: /2 a) 1+sin x sin x -dx integralini hesaplayını:

A: ∫0π2sinx1+sinxdxx = π-tdx = -dtlimits x=0→t = πx = π2→t = π2∫ππ2-sin (π-t)1+sin(π-t)dt

Q: intergrate the integral from 0 to 1 of (x^2 + x + 1)/((x+1)^2)(x+2)) dx

A: See the details solution in below

Q: 3(sin y- cos y)* dy cos y

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Q: a) Evaluate the indefinite integrals using Tabular Integration by parts. i) S(x² +x + 1)Sinxdx

A: Given: The integral  ∫(x2+x+1) sin(x) dx

Q: 10. f3, (x²-1) dx

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Q: Find the definite integral using the Fundamental Theorem. 1 dt NOTE: Enter the exact answer. dt %3D

A: To find the definite integral.

Q: 1) Find the indefinite integral f sec4 x dx using integral 77 from the reference pages in Stewart,…

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Q: Evaluate the integral. (Use C for the constant of integration.) integral of 2 cos(θ)…

A: To determine the value of the integral.