Find the value of (f o g)' at the given value. 22. f(u) u+3, u g(x) = Vx, x 1 (f o g)'(1) (Type an integer or a simplified fraction.)

Q: Q3/ Choose the correct answer to evaluate the following integral dx 1 1 o (1 – x*)ž 1- I = 4 r 2-1 =…

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Q: Q3. (30pt) Calculate the integral 2x³ – 4x + 1 - (1– cos x) dx 1+x? a) for n= 10 according Simpson…

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Q: By the even extension method applied to the function f (x) = e¬16x, where x > 0, the value of the…

A: We have to solve given problem:

Q: Find the most general antiderivative of the function g(x) 3x2 -e + coS I | O 6x-ex-sin(x)+C O…

A: The given function,  g(x)=3x2-ex+cosx  .................................(1)

Q: a) If | f (x) de f(x) dx = 2, find 1 (3f(a) – 1) de. = 7 and || - /4 (b) Estimate the value of the…

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Q: 1. Find all the antiderivatives of the following functions. Check your work by taking deriva (a)…

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Q: express L−1[F(s)G(s)] in terms of a convolution integral.

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Q: 8. Determine the value of n and h required to approximate r2 1 -dx x + 4 to within 10-3 and compute…

A: The value of h and n

Q: The integral J dx reduces to e+1 where u = f(x) and for some constant k.Compute f(1).

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Q: 3. Is the expression (ez+y+z +4x²y²2²)dx+(e²+y+z +r’yz²)dy+(e²+y+z+³y²z)dz = 0 %3D exact? If yes,…

A: Given expression is ex+y+z+4x2y2z2dx+ex+y+z+83x3yz2dy+ex+y+z+83x3y2zdz=0 To verify whether the above…

Q: x² = 10) Evaluate the integral S dx, x > 3

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Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

Q: A function is approximated by a cubic spline defined by: 25/12 30.0833 An approximation of ff(x)dx…

A: Sol:- Consider the function in the range of (0,1) ∫011+x+x2+x3dxApply the Sum Rule:…

Q: 5. Evaluate the integral f'(x) dx 1+(f(x))² given that f(0) =1 and f(1) = v3.

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Q: dx reduces to du The integral 3. ex + 1 where u = f(x) and for some и constant k . Compute f(1). (a)…

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Q: Q2) Evaluate the integral x dx a -0.

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Q: Use either integration by substitution or integration by parts as needed to evaluate S³= A B x²+1…

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Q: S(e-3y V6 + e- 3y 2y3+y -)dy y4+y2+1 -

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Q: Find the complimentary function and particular integral for (D² – 5D+6)y = e2x cos(2x).

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Q: Demonstrate that for the function of the type va? + x2 you use the substitution X-atane and use it…

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Q: What is the antiderivative of 1 / (x - (1/k)x^2) with respect to x? k is a constant

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Q: 2. Use the substitution u = x² and then Integration by Parts to evaluate / x³e**dx.

A: Given: ∫x3ex2 dx We substitute u=x2, that implies du=2x dx. By using this substitution, ∫x3ex2…

Q: 11.Use differentials to find the approximate change in f(x) = changes from x =1 to x = 1.08 V3 + x³…

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Q: 9. Determine the integral of the given function f(t) = t – it? for 0<t< 2.

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Q: 1. Find the antiderivatives of the following functions using substitütion ule. Write your a separate…

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Q: Q 4. a) Use integration by parts to evaluate Sz²cos zdz. b) Evaluate f xlog(x + 3)dx.

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Q: 2 3 2 Q5. Evaluate the value of integral |[xy'z dx dy dz . 0 11

A: I have stated the used formula in the solution

Q: (a) The Composite Trapezoidal Rule applied to the integral = | f(x)dx gives the error b - a E = - 12…

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Q: 21. Determine the general antiderivative of f(x) = 4x 4x4 + 9 2x2 a. 2 cosh +C 3 22 + C c. 2 sinh¯…

A: As per our guideline we are supposed to be answer only one question you can repost other question in…

Q: b Use the Substitution Formula, [f(g(x)) • 8 √ 4(Imx)³ dx X 8 3 $4(lnx)³ g(b) g (x))• g'(x) dx = […

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Q: Q2/Evaluate the integral: 1.57 9-x2 dy dx x, by changing the order of integration.

A: The integration order can be changed by changing the inner integral to outer and outer integral to…

Q: 11:32 E O 1 Evaluating the integral f In(x)dx, where x> 0 yields:

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Q: 39.: * Compute the integral: x (Inx) dx. a. (5e –1) b. (3e -1) c. (e +2) d. (5e -e') (e* -e) 32 16…

A: Use by parts integration

Q: Q2: find the antiderivative of the following a) S x + e* + sec(x) tan(x) dx b) /블dx x+1 c) S(e* + +…

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Q: Q2) Evaluate the integral x3 dx 3 a *0.

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Q: ,19 The estimate of an integral of of f(x) dx is given as 1860.9 using 1-segment trapezoidal rule.…

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Q: 11. Integrate the function. y? dy (49 – y²) 7y y + C V49 – y2 – sin y+C -1 - V49 - y2 | O A. O B.…

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Q: (b) Consider the integral I = f f (x)dx for the function f(x) = -2e + 4 1 x' +2x 120 Approximate I…

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Q: Find the value of the constant C for which the integral 6C x² + 9 dx X + 3 converges. C = Evaluate…

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Q: 6x 29. What is the particular antiderivative of f(x) = whose y-intercept is –4? 1 a. y = 4 ln |x² –…

A: We have to evaluate the above integrals.

Q: Q.1) Evaluate the following integral ez dx (2e2 – 4e* – 1) - -

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Q: Q2) Evaluate the integral x* dx 0.

A: To evaluate the given integral

Q: 26. (4D4 — 24D3 + 35D? + 6D — 9)у 3D 0. е"C, + с2x) + сз cosh }x + c4 sinh }x. ANS. y =

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Q: Q1. Evaluate the integral S dx (x + 1)(x² + 1)

A: We need to evaluate the following integral ∫01dxx+1x2+1

Q: dx - is 2/x - Sin| x +s|+c. Vx +5 The antiderivativeof - A) True B False

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Q: Find the value of the constant C for which the integral 5x 5C dx 2 X² + 1 Зх + 1 converges. C = 3…

A: Convergence of integral

Q: 1 In solving the antiderivative of f(x) = 2- sin(x) by miscellaneous substitution, the substitution…

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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: = "+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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