42–45. Symmetry in integrals Use symmetry to evaluate the following integrals. /4 r/4 42. tan x dx 43. sec? x dx /4 -T/4 r?x³ – 4x La - |x]³) dx 44. 45. 2x² + 1

Q: Q.3 Find the double integral for Sl. x2 dydx, where R between y = -4/x y = -x and x = -4

A: Ti evaluate the given double integral  first we draw  the region

Q: In the integral of x cos 2x dx with limits form 0 to pi/2, what is the indefinite integral? Select…

A:

Q: 2. Calculate the following integral: dx (a) sinh? x – 4 sinh x cosh x + 9 cosh² x +*) u (1– x²)² x…

A: 2) a)

Q: 13. Consider the integral | dx then (which statement(s) is/are correct) x2 - 4x 1 (i) -dx…

A: Given: ∫1x2-4xdx

Q: 2. Compute the following. When evaluating the definite integral, change the limits of integration.…

A: (a).  The given integral is: ∫x21+x35dx

Q: 6. (a) Determine the following integrals: S(16x³ + 6x? - + 50e* + 100)dx (ii) 40x(10x? – 5)² dx (i)…

A: Since you have asked multiple questions we will solve the first question for you. If you want any…

Q: -3.5 x/(16 – x²)3 dx 0.5 Find the numerical value of the integral using: a.) Trapezoidal Rule (n =…

A: Given: ∫3.50.5x16-x23dx To find: Numerical value using trapezoidal rule.

Q: '1 1 Given that x² dx = use this fact and the properties of integrals to evaluate (8 — бх2) dx.

A:

Q: 17. Evaluate the indefinite integrals. a) sin x cos x dx x +4 b) S dx (x2 + 8x- 7)2 c) S sin x dx…

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Q: Q.3 Find the double integral for Sle x² dydx, where R between y = -4/x y = -x and x = -4

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Q: 8. The integral What is the value of A. B. can be rewritten as 15x²x³43x - 19 (x + 1)²(x² - 6x +13)…

A: Let's find.

Q: A. Evaluate the following indefinite integrals using the Power Rule: 1. SE Va dx 2. S dx 3. S(-Vx +…

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Q: 5–22. Table lookup integrals Use a table of integrals to determine the following indefinite…

A: Question (5) - Let the given integral be y - y = ∫cos-1x dx          ..........(1)Let,x = cost…

Q: 3. (a) Evaluate the following integrals: (1) / 2x + 5 dx x – 3 (ii) / sin(tan 0) de cos? 0 = [ dt…

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Q: 19. Evaluate the integral Z √(x^2 − 9) / x^3 dx

A: firstly divide the numerator by denominator part by part to simplify the integration

Q: 6.2.24. Evaluate the integral. using integration by parts integrate 1 to 2 xln(x) dx   I am unable…

A: Use integral by part rule.

Q: 8. Depending on the real parameter p and q, what can you say about the result of the following im-…

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Q: (17) Given the following standard integrals 1 = arccosS + C /2ах — 2? a - and V2ax – x2 + C, 1 | dx…

A: Given data:   The first given integral is ∫12ax-x2dx=arccosa-xa+C. The second given integral is…

Q: Q1: evaluate the following integrals (choose 3) dx 1-f- dx V2x-x 13- 2x-x +[ (x* +x-2) cos 4xdx tan…

A: We are asked to evaluate the integral.

Q: 6.3.28. Evaluate the integral. using U substitution integrate (x^2)sqrt(x^2-1)dx

A: Use substitution method, to evaluate the integral

Q: 4 Evaluate the follwoing integrals. Show your work and state any appropriate methods you use. (a) 10…

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Q: -2 1 dx to Determine the minimum value of n required to approximate Jo x+4 within 10-5 by composite…

A: Given Integral: ∫021x+4dx to within 10-5 by composite Simpson's rule

Q: 5. S,(x-4)(x2-8x – 1)3

A: Solving the given integral.

Q: 6) Evaluate the improper integrals ∞ 5 a) 5² (+ + e-") dx s (-x) е 2 7 5 b) ² = 8 dx 4x-8 2

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Q: 3) Approximate the value of following integrals by using composite Trapezoidal rule, composite…

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Q: 2. Evaluate the indefinite integrals. (a) fx² - 2e*dx (b) Evaluate (3-4x)¹5 dx

A: We have to evaluate the indefinite integral

Q: dx integralini hesaplayınız. x(In x)

A: Fundamental theorem allows us to compute definite integrals using the antiderivatives. It states…

Q: 5) Find the follow ng integrals dx 5 Sin'x cosx de JT-6x assecextany dx d)J2-x dx e) change limits…

A: Since you have posted multiple subparts question in this question so I have solved first three parts…

Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

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Q: 2. Solve the following integrals using integration by parts: (a) / a² sin(x) dx, (f) / 2* In(x) dr…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: √ x² In(x² + 1)dx integralini Simpson's yöntemini kullanarak yaklaşık olarak hesaplayınız. Use the…

A: Given integral is ∫02x2lnx2+1dx. We have to evaluate the given integral by using Simpson rule. Here,…

Q: 2 Use properties of integrals to evaluate S [(e2") – (e*)] dæ, 1 2 2 if S (e2") dæ = $ – : dz = $ –…

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Q: Evaluate the integral - T/2 (8 + 4cosx)dx 0. Using:

A: The given integral is ∫0π28+4cosxdx In part (a), we shall solve it analytically, and in part (b), we…

Q: 1 2. Evaluate the integral using integration by parts. Hints: LIATE, 은(cos-1(x)) : dx 1-x² cos-(x)…

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Q: 8) Evaluate the indefinite Integral S x ³ √√₁₁ + x ²4 dx

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Q: 9/ Approximate the follwoing integrals using The Simpson's ruls @ 0-25 b (Cosx) dx -0-25 Š 0-5…

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Q: Q3. Evaluate the integral I = √_^₂(1 − x − 4x³ + 2x5)dx by; a. Analytically b. Single application of…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: 4. Determine the following integrals 4.2 - dx - a x

A:

Q: 1. Evaluate the indefinite integral. Hint: U-substitution. 3 dx x In x

A: ∫ 3x lnx dx 3∫ 1lnx·1x dx

Q: 1 c) (x² + e#)% ( Hint for part (c): Try to use Comparison Theorem for Improper Integrals) -d.x

A:

Q: Consider the improper integral dx . What is the appropriate solution and answer x2 + 2x +2 A lim…

A: We can solve given problem as follows

Q: السؤال 8 Evaluate the improper integral if it exists e'dx: - 00 -e.1 O e.2 O .3 0 The improper…

A: We will evaluate the integral and check if it converges.

Q: 4) Evaluate the following indefinite integrals. a. S (+ V3 - dx 4 3x2 b. S (2 sec2 x- 5 cscx cot…

A: Integrare

Q: 3. (а) Evaluate the indefinite integral 2Varctan(3x) dx. 1+ 9x² •16 (Б) Suppose we know that (3f (x)…

A: (a) We need to evaluate the following integral ∫2arctan(3x)1+9x2dx (b) We need to evaluate the value…

Q: 8. Which one of the following integrals represent the length of the curve y = x² - In(x), 1< x< 2 O…

A: (8). The given curve is: y=14x2-12ln x ,         1≤x≤2

Q: Evaluate the integral. dx (х — 4)(х — 8) (Use symbolic notation and fractions where needed. Use C…

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Q: 1. Evaluate the following integrals x² + 6x -dx (a) | x³ cot2(x4) cosec² (x*) dx, (b)|Tr3 – 10 – 5x²…

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Q: 1) Evaluate. Јx cosh ax dx 2) Evaluate the integral. (In x)² dx x3 1

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Q: 10. (a) Evaluate the following integral analytically. (b) Evaluate the integral numerically using…

A: The trapezoidal rule is used to find an approximated value of the integral. According to trapezoidal…

Q: Evaluate the following indefinite integrals. Show your solution. 1. f5 einx(sin x + cos x) dx ecos…

A: