1. Match the integrals (a)-(e) with their antiderivatives (i)–(v) on the basis of the general form (do not evaluate the integrals). (2х +9) dx x2 +4 хdx (a) ь dx (c) | sin x cos? x dx (d) x/16x2 – I 16 dx (e) x (х — 4)2 (i) sec- 4x +C 4 (ii) log |x| – log |x – 4| – -+ C (iii) (3 cosx – 3 cos x sin? x 30 + In(x² +4) + C (v) vx2 – 4+C -1 (iv) tan

Q: Q4) Solve the integral by Simpson's rule x3 cos2x dx, h 0.2

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

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Q: We have determined that du = 5x* dx. However, the given indefinite integral dx does not conta %3D x…

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Q: x³ + 6x² + x +2 fx-1 ax + In{(x + 1)*(x² – x + 1)| +- 2 Tan Ve The resulting integral of -1 + C,…

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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 Suppose we perform the substitution u=3+Vx in the integral dx . I (3+ Vx)4 What is the resulting…

A: we have to find the given integral

Q: 2. Evaluate the improper integral. e COs x dx

A: I=∫0∞ e-x cosx dx Integration by parts;Formula:∫(uv)dx=u∫vdx -∫dudx ∫vdx dxu=cos x, dudx=-sin…

Q: 3. Find the indefinite integrals. (a) /4 dx (b) /2* r 2x-x2 dx

A: Given two functions integrate it by use of formulae

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Q: 3 2 Evaluate the iterated integral x cos y dy dx. 2 3л 2

A: Ans= 5/2=2.5 For detail go through the solution...I have solved step by step in detail

Q: 1. In this problem, we will consider two methods that will allow us to evaluate integrals of the…

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Q: (4)Evaluate the definite integral (a)[ 1+sin x dx (b) | 2t + cost dt -7/2 5 x + dx (d)[ sec' 0 d0…

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Q: 2) a) Calculate the integral 9-x dx by using the 2 poner rule for antiderivatives: b) calculate the…

A: Solution:-

Q: Evaluate the 2 improper integrals attached with this question.

A: Given integrals are

Q: Which of the following integrals is NOT appropriate for a substitution method? A 5x*sin(x³)dx ®…

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Q: Q.2// Find (A) f sin¹ (x) cos5(x) dx (B) f 4t³-t²+16 t t² +4 dt (C) Use improper integral to find ²…

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Q: 2. Evaluate the integrals. (a) S (b) [9rc (c) J (d) O 1+ e²r 9x cot(x²)dx -do -dx cos sin² 0 +1 -dx…

A: As per the guidelines we can solve 3 parts only

Q: 13. If u(x) = sin 3x and v(x) = x, what are du and dv? Writedown  u dv and  v du in this…

A: Given- ux=sin3x and vx=x To Find- The value of du and dv, write down the value of ∫udv and ∫vdu,…

Q: Given dy – sin(x))dx + cos(x)dy, where C is the triangle with vertices (0, 0), (1/2, 0), and (t/2,…

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Q: 13. Evaluate the indefinite integral fx cos x dx x sin 2x cos 2x a. + c 2 x sin 2x cos 4x b. + c 2 2…

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

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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: -1 2x Evaluate the integral dx = 0 x*+1

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Q: Reduce to first order and solve. (1 - x2 )y" - 2xy' + 2y = 0, y1 = x. Use : fp dx = In [1/(1- x²)] ,…

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Q: !!! 6 cos (x2) Evaluate the integral -dx dy dz by changing the order of integration in an…

A: Triple integral

Q: Consider , xe¬**dx. What will be the appropriate solution and answer to this improper integral? A.…

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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: 1.0) Find the following indefinite integrals: 1.1) ∫ (5 + x7) (3x2 + x-4) dx

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Q: 3. a. b. Evaluate the following integrals 2dx dx cos²x√4 tanx - tan² x sin(√x)dx J I sin

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Q: 3 9-x 9-x2 Evaluate the integral dz dy dx. 0 0 . 0

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Q: 2- What is the solution for this integral? x²e¯* dx a) e-*(x² – 2x + 2) + C b) -e-*(-x² + 2x + 2) +…

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Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

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Q: I. Evaluate the following integrals. 3.x5 dx V2 – x3 1. - 2* + e2" sin(2") dx sin(2") 2. 2x + 3 dx…

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Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

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: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

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Q: 7. Evaluate the definite integrals: a) L, (x2 +1) dx b) 3x dx

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Q: 13. Find the integral using the u substitution method Jx(x+1)*dx

A: Solution of question as follow

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 indefinite integrals: a) S(2x + 3x -7x2 + x-5) dx %3| b) S(x – 5)² dx g)…

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Q: 2. Use symmetry to evaluate the given integrals. -200 A) S, 2x5 dx -200 В) cos х -п/4 B) S"/ cOS x…

A: A) ∫-2002002x5 dxB) ∫-π4π4 cos x dx

Q: 1. Compute the given integral. Using Substitution Method 5x-12 dx = +C 5x2-24x-1 *

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Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Evaluate the given integrals. 3x?dx 1. S 2х4-1 2 dx 2. S tan x(5+ln sin x) 3. Seš(6– ei)" dz 1 4. S…

A: according to our guidelines we can answer only three subparts and rest can be reposted thanku.

Q: 1. Evaluate these integrals either by substitution or by integration by parts: cln 2 et a sin(2r) dr…

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

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

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Q: 2. Evaluate the following Integral by using suitable method: 2y3 + y y4 + y2 + 1 dy -

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Q: A. B. Evaluate the following integrals using substitution method: (³-1) ²/3 √2 5.² 0 √r sin (1 + x²)…

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Q: = "+1 + C. 2. The power rule for integrals is x" dx a. Evaluate f da = fx2dx. n+1* 1 b. What goes…

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