Example 8.23. Evaluate using Gauss formula for n = 2 dx 1-1 1+x² and n = 3.

Q: 10. If n is a positive integer, then lim n- 0o N + (1/n)" 1+(2/n) can be expressed as + ... (A) |dx…

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Q: Compute - [In(4x² − 3)] d dx Note to type in a fraction it should look like (a)/(b)

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Q: The value of L(e" sinh(3t)) - 3. (-2) + 9 3 (8+2)ª + 9 3 (812) 9 O None of the choices 3 (-2) 9

A: The following Laplace formula are used in solving the given equation. Leat sinhbt=bs-a2-b2

Q: 3 (In x) Evaluate 8x dx. 25

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Q: xample 8.19. Use Romberg's method to compute ax correct to 4 decimal places. 2 0 1 + x²

A: Solution :-

Q: Example 8.13. Use Simpson's 1/3rd rule to find dx by taking seven ordinates.

A: Here we have y=f(x)=e-x2 now to take seven ordinate means n=6  (6 intervals) then step size…

Q: Example 7.13. Apply Bessel's formula to obtain y25 given y20 2854, y24 = 3162, y 28 = 3544, y 32 =…

A: Here we need to use bessel's formula to solve this problem.

Q: Evaluate the integral (4x -7/13 – 5x13)dx. „7/13 (4x -7/13 - 5x13)dx help (formulas) -

A: We first distribute the integration

Q: cos(x ) + æ5.1 dx. )ln(1+x² 3 cos(x Evaluate 1+ el.61x – 68 - 3. answer

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Q: X/Example 19-40. If U̟ is a function whose fifth differences are constant and if | U, dx can be…

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Q: 8 dx sec 2x-1

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Q: 6.5.8 Example H The equation 2yk V1– y? (6.111) Yk+1 = can be transformed into a simpler form by…

A: Given equation is  yk+1=2yk1-yk2                   (i) Eq. (i) is a non-linear difference equation.…

Q: 7 Calculate (6x + x²) dx, given the following. 8 7 218 dx = 3 7 169 dx%3D 3 x xdx = 12 5 7 (6x + x?)…

A: Explanation and solutions is given below.....

Q: 8 Suppose [g(x)dx =5 , and [g(x)dx =-3 , find the value of 2g(x)dx 8

A: We have to find the value of integration.

Q: 3 Find the general solution of the ODE x²y" + xy' -n²y = 0 for integer n.

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Q: Q3. Solve in terms of Bessel's function, the ODE: x²y" + xy' + ((Inx)² + y = 0 z = lnr using chan…

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Q: J 81 e dx %3D 81 e 5x 5x + e (Simplify your answer.)

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Q: Which graph represents f (x) = log, æ?

A: I have given an answer in step 2.

Q: Evaluate Inx 10 X 7 In x 10 dx = x dx. (Type an exact answer.)

A: Given integral:- ∫1710lnxxdx

Q: 8 3 9. Suppose that f(x)dx = 4. Find f(x)dx and f(x)dx. 9. 3 8.

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Q: 1. 2. 3. dx dt d²x + 7x = 5cos2t dt² d²x dt² dx +6 + 8x = 5sin3t dt dx + 8 dt + 25x = 10u(t)

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Q: Given f(x) = 8e²x df dx = Use parantheses when typing in the exponent.

A: Given that we need to find the f(x)=8e2x derivative of f(x). We will solve by using derivative…

Q: Let a be a constant. Given that -107 3x In(ax)dx = el8 ( 42 – 3. find In a. 3 %3D

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Q: = f(x + Find +6)(x − 2)dx + C

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Q: Evaluate the definite integral. 1²/² 70 2 1 - 4x² dx

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Q: J 1. Fin Find 2x³ (6 + x) dx TU

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Q: 4. 5. 1 X√(x)}² (x)²-49 dx 1 √9+8x-x² dx

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Q: 4. The value of A. 2 In x + 1 + B. C. D. 2 ln 2 ln 2 ln 2x² + 3x +3 (x+1)³ x + 1 + x + 1-1 x + 1|- 1…

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Q: 1.A.5. Show that in the range - <x<* 00 sinh kr Σ (-1)n-1 (24²) sin nx n=1 sinh kx = --²/4 where k…

A: (.) Given function is,   h(.)  Fourier series of a function  in the interval  i.e.  is given by,…

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