d.x (a) Evaluate the integral ; x In(4x) using the substitution u = In(4x). dx J r In(4x) +C -7x (b) Evaluate the integral dx using the substitution u = = –7x. -720 dx = +C

Q: Evaluating the integral f In(r³)dx, where x > 0 yields:

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Q: dx 6. Evaluate the improper integral. x² +3x+ 2

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Q: A u substitution has been used to evaluate the following integral. [ ²₁ f(x) dx = [₁, 2²( [²₁x² (7 +…

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Q: Consider the functions given.evaluate the integrals

A: First we try to write the given function using the mentioned functions.

Q: Using an appropriate substitution, 8tan-1x the integral J dx equals: 1+x2

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Q: Evaluate the integrals below: (-3) a) dx, b) cosy.eny. dx (xV(1 – (In4x³)² -2 -

A: in part b i integrate with respect to y because it is no sense of integrating with respect to x

Q: Evaluate the integral. dx a > 0 (a² + x²j3/2?

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Q: a) Evaluate the integrals using appropriate substitutions. dx Sino i)S i) f de Cos? 8+1 1+16x2

A: as per our guidelines I am solving only first question with both parts a(i) ∫dx1+16x2ii ∫sinθcos2θdθ

Q: Evaluate the integral dx (6х + 5)? y making the appropriate substitution: u = dx (6x + 5)2 II

A: Given query is to find the integral.

Q: 2 dx a) Evaluate the integral by completing the square and using a substitution 2 x2-6x+10

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Q: (a) Evaluate the integral using the substitution u = In (5x). x In (5x) dx x In (5x) ? Edit +C (b)…

A: An integral in some cases can be simplified using a substitution. For example ∫ln(x)xdx with the…

Q: Evaluate the integral. (Use C for the constant of i 4x2 + 3x + 4 dx (x² + 1)2

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Q: Q2 ) Evaluate the integral S*9/x7 + y²) dxdy.

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Q: Evaluate the integral VI- 1 /1 dy dx. – x² – y2

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Q: 1. Evaluate the improper integral or show that it diverges. (a)/ e* dx 8. (b) / dx (c) d.r (d) /…

A: If the limit exists and is a finite number , we say that the improper integral converges .If the…

Q: Which of the following is an improper integral? A dx -4 x² – x – 2 In3e (B cosx dx хе -2 dx C 2x + 8…

A: To find out the integral which is improper.

Q: Evaluate the integral. V4– e2¤ dx +C

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

Q: Consider the integral 3 4х f (x, y) dy dx 0, Evaluate the integral for f (x, y) = 5x²y

A: Given Data: Integrand: ∫03∫04xfx, ydydx Function: fx, y=5x2y3 Integrate the function. ∫03∫04xfx,…

Q: e2z Q5- The value of the integral . Sc Where C is Z =3 (Z+1)4

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Q: A. Evaluate the following integrals by substitution. 1. fx(2x2 + 3)%dx x5 2. S; dx (x6-8)2 3. Sx V1-…

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Q: Evaluate the integral f 2x (x? + 5)° dx using the substitution u = x2 + 5. 2x (x² + 5)° dx +C

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Q: The particular integral of (D² – 2D+ 1)y = xe® is 2 -2et - x2 3

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Q: 11 dx x2 +4 Evaluate the improper integral:

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Q: Evaluate the integral fe (2x+4) (x² + 4x + 2) dx n- by making the substitution u = x²+ 4x +2.

A: In the question we have to find the integral of the given function.

Q: Q3:Evaluate the integrals T|(x+y+1)dxdy -1-1

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Q: The sum 5 x) dx + -1, fx) dx can be written as a single integral in the form f(x) dx Determine a and…

A: Given query is to find the single integral fir the expression.

Q: Evaluate the iterated integral. 40 (xªy-7xy) dy dx 0-4 40 jjov (xªy-7xy) dy dx = [ 0 - 4 (Type an…

A: The given integral,    ∫04∫-40x4y-7xydy dx

Q: Consider the integral dx x . Using u-substitution, what is an appropriate u and du? -2x 2e

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Q: Which of the ff is equivalent to the double integral: a. f¹ ln(2x) − In(x + 3) dx b. ln(x + y) -…

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Q: Consider the integral 16–z² x? dz dy dx x²+y²

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Q: Evaluate the iterated integral. [²1²₂(x² - y²) dy d dx

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Q: Evaluate the integral. a dx 2 a > 0 (a² + x²)3/2' V2 92

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Q: Q6. A: Evaluate the integrals: sec x dx dx 2) L, | VIn(secx+ tan x) -2 (4+x²)3/2

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Q: Evaluate the integral x(x – 5)7/2 dx by making the substitution u = x – 5.

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Q: Evaluate the integral dx (2a + 6) by making the appropriate substitution: u = dx (2a+ 6)°

A: I have use the substitution

Q: +00 dx Evaluate the improper integral x(In x)²

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Q: e2z Q5- The value of the integral . Where C is Z = |3 (Z+1)*

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Q: (b) Consider the integral I = So f(x)dx for the function 1 f(x) = -2e-* + 4 2x 120 Approximate I…

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Q: Evaluate the integral. V16-a? 1 dy dx dz = -V16-x2 (x2 + y?)1/2 -4.

A: We can solve as follows

Q: Evaluate the integral dx (2x + 6) by making the appropriate substitution: u = dx (2a + 6)°

A: To evaluate the given integral.

Q: c4 So So (6x² +9y²) dx dy

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Q: Consider the integral dx then (which statement(s) is/are correct) 2 -4X 1 (1) z In(x-4)-Inx]+C when…

A: We find the integral of ∫1x2-4xdx by using partial fraction and completing the square .

Q: x? Use the residues to evaluate the improper integral: -dx . (x² + 1)(x² + 4)

A: According to the given information, it is required to evaluate the improper integral using residue…

Q: dx The integral can be rewritten as VT - x 00 lim (-2+ v1– 3) S--00 lim (-1+2v1– s) s--00 B lim (-2+…

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Q: 6 r5 So f5x dy dx X 1

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Q: Q15. Evaluate the integrals 1. (x² + y² + z?) dz dy dx

A: We have to evaluate the integral.

Q: Find the integral 1 dx J x² + x + 4 +C

A: ∫1x2+x+4dx Consider, x2+x+4=x2+x+14+154=x2+2x12+122+154=x+122+154     ∵a+b2=a2+2ab+b2=x+122+1522

Q: Evaluate the integral 2x (x2 + 3)° dx using the substitution 6 u = x + 3. | 2.x (x² + 3)° dx +C II

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Q: Evaluate the integral. (Use C for the constant of integration.) R - 9x In(x) dx x² – 25

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Q: A. Evaluate the following integrals 1. 2. L. 3. , e*dx dx dx -1 x2/3 4. SE tanodo -4 dx

A: solution:-Q.(4) ∫-∞π2tanθdθsolving the improper…