Calculate the primitives of the functionf: D R, using the table of undefined integrals and their properties a) f(x) = x-5 b) f(x) = sinx - 3e* + 5 %3D c) f(x) = 2x2 + 8 - ! %3D d) f(x) =Vx e) f(x) = %3! 6x n f(x) = (x- 4)²+2 %3D

Q: The integral 4x dx Vx2 – 4 1 is an improper integral of typel is an improper integral of type II…

A: The given problem is solved below in detail.

Q: Evaluate the integral of (3x2 + 9y2) dx dy if the interior limits has an upper limit of y and a…

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Q: Find Lebesque integral of function on segment (-3,0) 1 f(x) = %3D x+3

A: Given, fx=1x+35 Let, A be the set of all rational number in -3,0. Here, mA denotes the Lebesgue of…

Q: Find the solution in the form of Fourier integrals: Ut- 3uxx = 0, u(0, t) = 0, |u(x, t) bounded as x…

A: As per the question we are given a initial boundary value problem as : ut - 3uxx = 0 And we have to…

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate the integrals in Exercises 25–30 by using a substitution prior to integration by parts.…

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Q: What is the resulting integrable form of evx+I x+1

A: We have to find value of given Integral.

Q: Use the properties of integrals to verify that 2 < V1 + x² dx <2/2

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Q: 14. Verify that f cotx dx = In(sin x) +C. (Do not try to solve the integral from scratch.) %3D

A: Given: verify that ∫cotxdx=lnsinx+c For verifying given integral, we integrate given integral

Q: The integral 2 X dx 2 - Vx² – 4 3 1 is an improper integral of type I (3)% is an improper integral…

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Q: Evaluate the integral using formula 35 (from the 1-page differentiation & integration formula) by…

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Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by = - 2n…

A: The fourier integrals of two continuous fx and gx defined on ℝ are defined…

Q: Сompute L f dx, where f(x)=|x|.

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Q: hat should be the rewrite of the integrand of ((2x+5) dy so that the resulting integral is…

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Q: evaluate the integral (Usec for the constant af mtegration) (Xt 6x) cos (x) dx

A: Use the integration by parts to simplify.

Q: Use trapezoidal with 3 level romberg (k=3) to evaluate the integral from lower limit 0 to upper…

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Q: Evaluate a. Fв- x-3Dаx

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Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: b. It is known that on the integration interval -1 <x< 3, for the integrand function f (x): 2.2 <…

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Q: Find the integral of * dx 2 sin x – cos x - |tan + 2 + v5 + C tan + 2- V5 In | tan + 2+ v5 |tan + 2…

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Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: Is the integral of 2x wrt x equal to 2x^(1+1)/(1+1)?

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: 3. Compute the line integral of F(x, y) consisting of the line segment from (T,0) to (2, 5),…

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Q: Evaluate the iterated integral: dydx - 1/4 Jx2

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Q: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

Q: Evaluate the integral ∫(5x -1)2 dx by two methods: first square and integrate, then let u = 5x - 1.

A: To evaluate the integral ∫5x-12dx

Q: Use the Midpoint Rule withn= 3 to approximate the integral %3D 13 (- 9z - 3a")daz 9x 3x) dx

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Q: What should be the rewrite of the integrand of dx so that the resulting integral is integrable?.…

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Q: Compute the integral of f(x) = 0.3 – 2x² + 40x³ from a = 0 to b = 0.8 using i. Trapezoidal Rule with…

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Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

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Q: The double integral; ) dA Sin(x2+y², (4+X2+42)- 2. is it convergert this regon; Conu in {x20,y>OS

A: Now, we need to verify the convergence of the above integral.

Q: Find the integral of * dx J 2 sin x – cos x tan + 2 + V5 + C tan+ 2- V5 V5 |tan + 2-V5 V5 In tan+ 2+…

A: Option 2 will be correct choice.

Q: 4. Calculate the indefinite integrals for the following functions as integrands (section 8.3): 1 (a)…

A: Recall: ∫x2-a2 dx=12xx2-a2-12a2logx+x2-a2+C

Q: 9. Use Simpson's Rule to approximate the integral f Vx3 – 1 dx withn = 6.

A: We have to find the value of given integral using Simpson's rule.

Q: 11)By using Tabular integration solve the integral f x³ 2* dx A)Sx³ 2* dx = x³, In 2 2* 3x2 2* 2* +…

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Q: I need help understanding/ solving attached question for CALC.

A: Given the two parametric form of the line segment from (3,0,1) to (1,4, -2).

Q: 8. [In(x² + 1) dx

A: Formula for Integration by parts: ∫fg'=fg-∫f'g

Q: et dz V1-e2x

A: Given problem:-

Q: S(3x – 2)(x + 1) dx

A: First multiply the expression under Integral then integrate and put the limits

Q: Consider the indefinite integral " (5x³ + 4x² – 75x – 68 22 – 16 da Then the integrand decomposes…

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Q: Evaluate the iterated double integral JI-X² ( [√x² sin (x² + y²) dz dy dx

A: A a couple of imperative is a specific imperative of a characteristic of numerous actual variables…

Q: Evaluate the integrals in Exercises 1–6. (sin¬l x)² dx 1. dx 2. x(x + 1)(x + 2)· . · (x + m) 1 /sin'…

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Q: 2. xem di

A: The given integration, ∫xe3xdx use integration by parts, ∫u dv=uv-∫v du use the formulas,…

Q: 2. Calculate the indefinite integrals for the following functions as integr 1 (a) x In r/(In x)2-1…

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Q: NN² 4xy² dydx /4-x2

A: In the given question we have to draw the region of the integration s.t…

Q: Evaluate the integrals in Exercises 1–8 using integration by parts. In x dx In (x + 1) dx 1. 2. |dx…

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Q: Consider the definite integral. (18x – 1) e9x²-x dx Let u = 9x? - x. Use the substitution method to…

A: We have to find the integrand after substitution.

Q: Compute the double integral of f(x, y) over the domain D indicated. f(x, y) = 21 sin 23x; bounded by…

A: The double integral to be evaluated is  ∫x=0x=π46∫y=0y=cos23xfx, y dydx, or, ∫x=0x=π46∫y=0y=cos23x21…