approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

Q: integral (cos(x)^1/2)dx

A:

Q: .3 1 -dx using the midpoint rule with three subdivisions to four decimal In(x) Approximate places.…

A:

Q: sin(x) + 2 x4 +1 5. Determine if the integral dx converges or diverges.

A: Cauchy integral test : For an>0,let ∑n=λ∞an is a series of positive  terms. Then ∑n=λ∞an is…

Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

A:

Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

A:

Q: 14.Use a substitution to evaluate / aVx+1 dx rVa+1 dx. Show all details of the process.

A: To solve- given integral by substitution  method.

Q: 18 dx Integrate using trig. Substitution: S- x² V9– x²

A:

Q: dx 2√√x + √x

A: Solution of given question is written in below steps.

Q: Evaluate: 1-11-24 = - dx 1 + x 0 By the trapezoidal rule with h = 0.5, 0.25 and 0.125 respectively.

A:

Q: Evaluate f x² cos 4x dx Evaluateſ sin* 3x cos3 3x dx Evaluate the integral J x²+x-1 dx x(x²-1)

A: Given:   i) ∫x2cos 4x dx      integrate by parts ∫fg'=fg-∫f'g     here f=x2,f'=2x , g'=cos…

Q: integral (dx/(√(x)+x))

A:

Q: linear a approx Imation differential's to estimate Ja6.96

A: let ,

Q: 19. x'dx √√5x² +4 -S

A:

Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

A:

Q: Evaluate (indefinite integral) (4x^2.5 - x^e - 2sinx)dx (t^3 + 5t^2 - 4)/ (t^2) dt

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Q: x +1 -dx x² (x – 1) (a) Integrate

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Q: dx x+x4/3

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Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: R(x) = F/2 π dx

A: We have to evaluate the integral: R→x=∫0π/2sin2x3x+1, lnx2-1,xx2+1dx   .....(1)

Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

A: derivative

Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: INTEGRAL OF e^(ln tan^2(x)) ln e^(cos(x)) dx

A:

Q: Che number ofunits in Z31[x] is

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Q: (a) Evaluate the indefinite integral (anti-derivative) x°(1+ 2*)® dx by using the substitution u =…

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Q: (a) Evaluate xe* dx using substitution method. (b) Evaluate | 6xe* dx using integration by part…

A: We will find out the required value.

Q: integral of (e^2x)(sin3x) using u=e^2x

A: Given, ∫e2xsin3xdx    We have to find the integral

Q: Using integration by parts, | - | x sin(x²) dx x* cos(x²) dx = k – Then k is?

A:

Q: 9. S sec³ x tan x dx

A: Given ∫sec3xtanxdx We know that  ∫secx.tanx=secx + c ∫xndx=xn+1n+1+c

Q: integral e -x cos 2x dx

A:

Q: IV. Integration by Part 1. | sin x sin 4xdx Scos cos 2x sin 3xdx 2. 3. (sin(In r)dr

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Q: Integrate f dx using integration by parts. x+1

A: Please refer the attached image for complete solution.

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Find complementary function and particular integral of d²y - y = xe* + cos² x dx2

A:

Q: x2 Use integration tables from the back of the text to find the integral f- dx. Specify which V5-4x…

A: Given,    ∫x25-4xdx We need to solve this integral.

Q: Use integration by parts to derive a reduction formula for x"e dx. Use the result from part 1 to…

A:

Q: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

A: Since the required point is 0.001 near to 0, so we approximate linearly about x=0, also at this…

Q: Estimate the value of df/dx for f(x) = root 8x at x = 3, using any method

A: To find the derivative of f(X), differentiate with respect to X on each side.

Q: Uniclaretiana Fundoción universitaria Claretiana 1 (In x - 4) dx – (x + 1) dy = 0 2 4 +6x) dx +…

A:

Q: The actual error of the approximation of I = x² sin (x³) dx using composite Simpson's rule with n=4…

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Q: Use integration by parts to derive a reduction formula for x"e- dx. Jse the result from part 1 to…

A:

Q: Let y = 5(square root x) Find the change in y. Delta-y when x = 5 and delta-x = 0.1 Find the…

A: The given function is y=5x. We need to find ∆y when x=5 and ∆x=0.1. Also, to find dy when x=5 and…

Q: dx (5-4x-x²) 18. 8. f

A:

Q: 1 B3. Evaluate dx, using substitution method.

A:

Q: 34. e4x cos 2x dx

A: Solution:Given∫ e4x cos 2x dxFormula:∫udv=uv-∫vdu∫sin ax dx=-cos axa+C∫cos ax dx=-sin axa+C∫eax…

Q: | (In x)² dx_use integrationI

A:

Q: k. f(x)=cosh(x³)+ sinh(10x) 1. f(x)=In(x* +1)

A:

Q: 1. Find the numerical Integration of cos(x) + sin(x) where n = 4 using trapezoidal rule.

A:

Q: alue of A can be calculated based on f(x)dx = 1.

A: The given probability distribution function is,

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.