4. Calculate the following integrals by using the integration methods. (4x* + 8x3 + 15x)dx (a) dx (b) ; sin x· cos? x Vx2 + 4x

Q: Which of the following cannot be evaluated directly by a basic integration formula? ver Vex - 1 dx…

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Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

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Q: I. Find the following integrals. – 8x +5)dx 2. [(-6x' +9x² + 4x - 3)dx 1.

A: 1. Consider the given integral. I=∫5x2-8x+5dx

Q: 3. Find the following definite integrals. (2x +3)dx (x2- 1)dx x² - 2x)dx sin(3x + 4) dx 1

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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: 1. Find the following integrals. i) S 3e-2x dx 2x2-1 dx ii) S: 2x3-3х

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Q: b) Evaluate the following integrals using tabular integration by parts » [ax* 2) [(x² + x + 1) sin x…

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

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

Q: Evaluate the integral. (Use C for the constant of integration.) x² + 9x + 1 dx (x² + 1)2

A: Make two parts of the integration.

Q: Use MUPAD to determine the following indefinite integrals (7.1) (7.2) (2ax-x²)³ dx. S (7.3) Obtain a…

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Q: 7. Evaluate the integral using integration by parts. S cos (5x)e 2* dx.

A: Given the integrationI=∫cos(5x)e2xdx

Q: 6. Which of the following integrals cannot be evaluated using integration by parts? A. ſe-*sin2x dx…

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Q: 4) Evaluate the definite integral: S, (2x² – 4x + 6)dx. -

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Q: 2. Identify which of the following integrals are improper: 1 1 dx 1 fin(x)dx 1 X +3 1 fe* dr -dp- 3

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Q: Determine the following integrals: 1.1 G 3x³ +8 X dx 1.2 G 1.3 4x+6 dx x + 3x-10 sec² (sin 5x)cos 5x…

A: We have to find out solution

Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

Q: b) Evaluate the following integrals using tabular integration by parts 1) (3x2 - x + 2)e* dx 2) |…

A: Evaluate the given integrals  1.∫3x2-x+2exdx2.∫x2+x+1sinx dx3.∫8x4cos2x dx using tabular integration…

Q: Q2. Use integration by parts method to evaluate the following integrals. 1. dx 2. S cos x? dx -dx 2…

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Q: 2. Evaluate the following double integral by first reversing the order of integration. (6x-y) dx dy.

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

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Q: 4. Calculate the following integrals by using the integration methods. 1 (4x* + 8x3 + 15x)dx Vx2 +…

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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: 2. Evaluate the following integrals. a) [ex.sech (e2x + 1) dx b) [sech (2x-1) dx c) Vsinh 2x…

A: Integration by substitutions

Q: Evaluate the integrals ∫cos (1 - ln y)/y dy

A: We have to find the integrals: ∫cos1-lnyydy We will find this integrals by substitution method Let…

Q: Q1. Evaluate the following Integrals 1 dx 1- cos x .2 +x - 2x +3 dx

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Q: 6) Use the successive approximations method to solve the following Volterra integral equation: u (x…

A: The Volterra integral equation is given as u(x)=x22-∫0x(x-t)u(t) dt. We have to solve the equation…

Q: 9) Calculate the following integrals using the change of Variable (substitution) mothod: 96) 3+2 dx…

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Q: 14 Find the integrals using integration by parts. xp_ († +x)xf • - dx c. fr'e"de e flnx'de d. f (in…

A: Solution: The objective is to find the value of the given integral

Q: 4. Calculate the following integrals: 4 3 dx 1 – x2 dz 25z2 + 1

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Q: 4. Evaluate the following integral by first reversing the order of integration dx dy.

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Q: 1. Set up the following improper integrals by definition. sin(x) dx 22 — За — 4 а. xe dx с. 4 et b.…

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Q: Evaluate the following indefinite integrals. 1. S(5x + 4)11 dx 2. Sx (x² + 2)17 dx 3. fx²(9 – x³)5…

A: The solution is given below

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: Show detailed solution to the following using ti integration. x'dx 1. Integration by Parts J Vx4-5

A: Let's find.

Q: J sin(lnx) dx

A: Let's solve given integration.

Q: 4-Évaluate the following integrals a) In dx b) ] ()"- dx 5/2 tan x

A: Integration:   The collection of all antiderivatives of f is called indefinite integral of f with…

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

A: Solution of question as follow

Q: 1. Evaluate the integrals below. 5x²-x +3 (a) J x³ + x (b) [√v √√√x – 1 dx dx

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Q: 3. Apply Romberg quadrature to •1 1 dx 1+ x2 for h = 1, 1/2, 1/4, 1/8. Show a table of approximate…

A: We are given the following definite integral : ∫1/(1+x2) dx from 0 to 1 And we have to solve it…

Q: b) Evaluate the following integrals using tabular integration by parts 1) (3x² – x + 2)e* dx +x + 1)…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: 2. Reverse the order of integration and then evaluate. So S, x² sin(xy)dxdy а.

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Q: 3+n (2x) dx By specifying the +ype of examine it by explainings conveyere integral, x --

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Q: 02: Evaluate the following integrals: secxdx 1. S- VIn(secx+tanx) 3. VInn 2xex² cos(e**) dx

A: Use the substitution method to solve these problems.

Q: 7. Integrate the following indefinite integrals. 3e5x dx 1-2e5x a.

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Q: Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

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Q: evaluate the given integral.

A: The given integral ∫2x+1xx2+4dx can be evaluated as, ∫2x+1xx2+4dx=∫2x2+4dx+∫1xx2+4dx The integral…

Q: 1. Use Numerical methods to approximate the following integrals (a) (x +y)dxdy , n = m = 3

A: Trapezoidal rule: ∫cd∫abf(x, y)dxdy=h2fa, y+2fa+h, y+fa+2h, y+⋯+fa+n-1h, y+fb, ydy, where h=b-an.…

Q: 1. Find the exact value of the iterated integral by changing the order of the integration: 8 2 1…

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Q: Which of the following integrals are improper? (Select 3 L₁x²-1 dx 3x - 1 1 06²/21 x ² = 1 dx 2x 00…

A: Topic:-  improper integration

Q: Evaluate the integrals below. 4 x+6 dx 1 VX TE/7 a. b. " sin(t) dt J/3 c. x Vx3 +2 dx

A: As per guidelines, we have to solve only first three subparts. The given integral are: a. ∫14x2+6xdx…