2 1. Find the indefinite integral. Sáre 4x2 | 6xe dx 3 4x a. 2 3 4x2 +C c. 4&r°e*x*+C 2 4x2 +C +C b. +C с. 4 4x2 3 4x2 d. 24xe4* + C e. 4 xet +C 107t

Q: 4 3 12 2 cos (x2) 3Vz Evaluate the integral|| dx dy dz by changing the order of integration in an…

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Q: 14 Find the integrals using integration by parts. a. fx(x + 4) dx c. fx'e"dx e flnx'dx d. [(In x)°…

A: (g) The given integral is, I=∫lnxxdx Rewrite as, I=∫xlnxdx Here, ∫udv=uv-∫vduu=lnx and du=1xdxdv=xdx…

Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

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

A: Given two functions integrate it by use of formulae

Q: 2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in…

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Q: Solve the integral: A B с 1 √√x+x √√ Sin/1+x²|+c -In +C 6in|5+ x²|+C с {in/1+x³ |+c C dx

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Q: 7. Express the solution of y" + 2y' + 2y = sin (3t) convolution integral (you don't need to evaluate…

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Q: Find the indefinite integral. |cos 2x ein 2* de sin 2x A) 2 +C ein 2x +C B) C) sin 2x e cos2x +C D)…

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Q: 2.Find the following indefinite integral without substitution. S sec y (tan y- sec y)dy

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

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Q: (6x³ + 3x? x² – 16 89x – 52 dx Consider the indefinite integral Then the integrand decomposes into…

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Q: 1. What should be A for the path independent of (2,4) xy + A 2Лу — х dy y? -dx + (1,2) Moreover…

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Q: Find the indefinite integral. 1. 16 + t² dt * (x² + 4)³/2 + 4)3/2 2. -dx-

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

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: For x 1/2 -dx and using the substitution u=x 1/2, the resulting integral takes the form: x-x 4u -du…

A: We can rewrite the given integral by using this substitution u = x1/2

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: 3 Which of the following is equal to / sec 2 x tan³x dx to obtain the correct indefinite integral? A…

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Q: I.Evaluate the ff. iterated integrals. еЗл /2 сл /2 2. cosysin2x dy dx

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Q: Solve the integral (5x - y)dx + (2x + cy)dy along the curves x = y3 from (0,0) to (1,1)

A: Explained below

Q: 2/3–2 dx integralinin değeri x² + 4x + 8 aşağıdakilerden hangisidir?

A: The integral can be solved using completing the squares method. Since the integration is definite…

Q: Evaluate the iterated integral. 7 8 (x² + y² + z²) dx dy dz -6 0 0 7 8 (x² + y² + z² )dx dy dz =

A: Given that: ∫-66∫07∫08(x2+y2+z2)dxdydz

Q: Solve the Indefinite Integral. xe²t S dx (2x+1)² A [1-21] +0 e2x 2x C 4 2x+1 B. 2-2(22+1) + C 4 C.…

A: SOLUTION-

Q: please explain how to do question 7c

A: The given integral is ∫(1-3x)4dx.

Q: 5. Express 0 lim E (5x2 – 9x +16)Ax;[ – 8,4] as a definite integral. L (5x – 9)dx b. l' (10x – 9)dx…

A: The given sum is lim∆→0 ∑k=1n5x2-9x+16∆x; -8, 4. The given limit can be expressed as the integral of…

Q: 15. Evaluate the given integral, V4 – 9x² dx: arc sin () A. x V4-9x2 2 arc sin () x V4–9x² В. + c 2…

A: Giiven: To evaluate the integral∫4-9x2 dxFormula: ∫a2-x2 dx=x2a2-x2+a22 sin-1xa+c

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

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Q: 10.) Find the integral of* 3 (-4y ) ( +14y-7) dy

A: We need to evaluate ∫3y6-4y-3y7+14y-2-76dy                          (1) Let y7+14y-2-7 = t On…

Q: Q.2. Calculate the integral of: f(x) = (3x+1) from a=-0.2 to b=0.6 by using Simpson's Rules only and…

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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: 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: a) Find the indefinite integral of the function 1 y = 3t2 + 2e3t +- + 2 cos 3t | b) Calculate the…

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Q: find the indefinite integrals. 1. ∫ e−0.05t dt 2. ∫ (3/t  -  2/t^2)  dt

A: case 1:The given indefinite  integral  is ∫e-0.05t dt.Let u = - 0.05t, then du/dt = -0.05.

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: Evaluate the integral. S(e* +8e -*) dx | (e 4x +8 e -x) dx =[(Use C as the arbitrary constant.)

A: Consider the given integral.

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 dydx -23-1 (xy)³ SS.

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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: aluate the integral / (8 x + 18y)dx + (24x – y)dy alor y = x² from (0, 0) to (1, 1). TE: Enter the…

A: Topic:- application of integration

Q: Evaluate the iterated integral. 5 6 7 ||| ? +y² + 2) dx dy dz -5 0 0 5 6 7 | || (1²+y² +²)dx dy dz =…

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Q: Evaluate the integral. 고-36 x² – 36 . 6cos- (승) +0 /x² – 36 - dx = Vx² – 36 – 6cos¬! + C x² – 36…

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Q: Find the general indefinite integral: 1) S(x13 + 7x².5)dx 2) S Vx5 dx 3) Sv(v² + 2)²dv 4) Sx³cos(x*…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

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

A: Integrare

Q: Solve the problem. Rewrite the integral 5(1 - z/6) 2(1- y/5 - z/6) dx dy dz in the order dz dy dx.

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Q: How do I find the definite integral of these problems?

A: (a)

Q: Consider the indefinite integral Ва3 + 21? + 5а + 0 dx x² – 1 | Then the integrand decomposes into…

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Q: ∫(−2x2+6x−6)dx   Select the correct answer below:   a. 2∫x2dx+6∫xdx+6∫dx   b. −2∫x2dx+6∫xdx+6∫dx…

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Q: 7. Find the indefinite integral. 1. dx V9-16x? 4x 1 tar arcsin 3 +C_b. arcsin(9x) +C a. 4 4x c.…

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.