6. Complete the square to get an equivalent expression: 7-6x – x² No integration necessary on this one!

Q: Evaluate the integral (2æ + 6)(x² + 6x + 9)*dx by making the substitution u = x? + 6x + 9. + C

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Q: The result of the integration sign(t-t)8(2t - 1)dr is 1 A. B.sign(t -) C. 5(2t+1) D. sign(t +

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Q: Find x" In x dx; n # -1, n real. (Use C for the constant of integration.)

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Q: Rewrite the integration in terms of u. 2x dx = du x² + 16

A: Given :∫032xx2+16dx

Q: Using a computer algebra system, it was determined that x10 &r° 35x. 56x [x(x + 1)8 dx = 7x 2 + &x7…

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Q: 3. Solve for the values of "x" in the equation f (x) = x +, using (a)Bisection Method, %3D (b)Secant…

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: Evaluate the integral |(2x + 6) (2² + 6x + 6)°dx by making the substitution u = x² + 6x + 6. + C…

A: Indefinite Integration

Q: Evaluate the integral. x dx (7x° + 3)* 5 (7x² + 3) * + c -4 O A. 56 7 O B. -(7x + 3) - +C Oc. -(7…

A: Given query is to find the value of the integral.

Q: State ALL the theorems on integration used in the following computation: 23 | (3r² – 5)dz = 3 dæ =…

A: Integration is a method of bringing disparate parts together to form a whole. The sum-difference…

Q: Solve the separable equation using the integral factor  y⁴ y¹ +y¹ + x² + 1 = 0

A: Given equation is y4y'+y'+x2+1=0solve it

Q: -8 1 The integral dx x2 + 64

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Q: the integrating factor of the non exact DE ydx-xdy=0 is -1/x^2,show your solution

A: We will solve the problem

Q: Calculate the integration from the following figure y 2 y=x-4 A

A: To evaluate the integral for the region shown

Q: dæ 2 (x² + 1)²

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Q: Evaluate the following using an appropriate technique of integration. 3x +1 xp- (x² + 1)(2x – 1) (c)

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Q: Find the integration factor and use it to find the general solution of the eqation  ( (y(x)2) )/2 +…

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Q: %3D 0 = fipfiz + zp(z+ f+z=)

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Q: Evaluate the integrals a) dr 24 dy Vy-16 c) x+3 2x- 8x (b)

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Q: 2 V4 – x²dx 0.

A: A detailed solution is given below

Q: 2x sec(5x) tan(5x) dx can be evaluated using integration by part The integral expression udv =uv the…

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Q: Find the integral 17T dx 2+18 1 는시17x + 18+c 17 1 18x - 18 +c b.

A: Solve by substitution integration method

Q: Evaluate the integral 4 + 4) (x² + 4x + 2)*dx by making the substitution u = x2 + 4x + 2. + C NOTE:…

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Q: Given the integral J6x2 - 4x dx бх2 - 4х

A: Complete the following question involving basic integration techniques. Given the integral…

Q: 5y + 5 5 dy 2y e - 5

A:

Q: Solve the following PDE using the method of separation of variables and Fourier:

A: In this question, we solve the given boundary value problem by using the separation of variable as…

Q: Use the substitution formula to evaluate the integral. Vx +1 dx B) 2/2 - 1 D) 3/2 - 3

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Q: Evaluate the integral *(2* – 3)*da a* – 3)' by making the substitution u = x* – 3. | +C

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Q: Evaluate using a table of integration formulas. 5 dx 24) XV36 - x2 X-6 +C X +6 A) In +C B) In 12 6 -…

A: Solve the following

Q: Evaluate the integral : S 8x2+10x-6 (x-1)(x+1)z dx (2—1)(ӕ+1)? +C

A: Given: ∫8x2+10x-6x-1x+12dx To do: Evaluate the given integral.

Q: Show that 3x2 +6x +2 = 3 (x+1) - by completing the square. Hence, evaluate the 2 integral dx. V3x? +…

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Q: %23 %24 In using the technique of integration by parts, you must carefully choose which exp…

A: Given ∫x7 cos(8x)dx

Q: (4) Recall the formulac: (5) Find the integrals: • ftan² (x) dx t: Is ta SC

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Q: d Calculate the integral 2r -x

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Q: 3. 2 1 What is the value of the integral 7xyz² dxdydz ? 0.

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Q: Solve using product rule d(uv) = u dv + v du: f(x) = (x^2 + 4) (x^4 – 4x^2 + 16)

A: Given that, fx=x2+4x4-4x2+16 Differentiation formulae: ddxuv=uddxv+vddxu    [Product rule]…

Q: dx 2 28 — 12х — х

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Q: What is the integrating factor of 2 (y- 4x) da + rdy + xdy = 0? O 2x

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Q: The result of the integration sign(t-t)6(2r- 1)dr is 1 А. B. sign(t- C. 8(2t+1) D.sign(t +)

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Q: Solve the separable equation using the integral factor  2xy + 6x + (x²-4)y¹ = 0

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Q: Evaluate the following integral. x² - 6x +9 dx (27 + 6x-x²) 3/2 Rewrite the integrand by completing…

A: Solve the given integral

Q: Find the integral. 12x Vx dx 9 24 OA. 7 +C 8 О в. + C 3

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Q: | Væ – 2 dæ 2

A: Given: I=∫26x−2dx

Q: df Use integration to find f(4), if = dx O -26.667 O -19.667 O 26.667 O 30.333 5x2, and f(1) = 7.

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Q: 2) I = S t? sin ßt dt

A: Standard Formula that has been used are ∫sin(ax)dx=-cos(ax)a∫cos(ax)dx=sin(ax)a

Q: Evaluate the integral: [(4 t³ - 9)i+sec² t (t³+4)3 k]dt +

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Q: Solve the following DE using Separable method. 2y' = x(1- y')

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Q: 2x2 + 2x + 11 dx (2x + 3)(x² + 4) (c)

A: Evaluating the integral using partial fractions.

Q: Calculate the double integral. 3ху2 11 3xV²_ DA, R = {(x, y) 10 ≤ x ≤ 3, -2 ≤ y ≤ 2} d R + 1

A: We have to calculate the double integral∬R3xy2x2+1dA R={(x,y)∣0≤x≤3,-2≤y≤2} In order to find the…

Q: Find the definite integral c2 2127 dx z13z2 1

A: