A tabla of value: for , 2. arc o'is give. g(x) f (x) 9'(x) (a) Ir nix) = gx, find SY1. %3! (b) if MN) = gfx), frd H(1). HY1) -

Q: Find the length of the curve using formula.  y= ln (cosx) bounded by 0 and pi/4

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Q: The following problem is for extra practice and does not have to be submitted. 2 1 -dx using the…

A: According to question ∫0211+x3dx,       n=4

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Q: Find the length L of the arc formed by y=e^4x/4,0≤x≤3

A: To find the length L of the arc formed by y=e^4x/4,0≤x≤3

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Q: The antiderivative of ∫ 1 / √(1 − x2)  dx can be either arcsin x + C or −arccos x + C. Does this…

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Q: 1 dz, by Simpson's -rd rule, using 8 subintervals, correct to four Problem - 26: Find the value of…

A: According to question given that∫3515x+7dx, n=8

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A: Given integral is ∫-4-1 -x4 -10x3 -24x2 -4x+4 dx Take  fx = -x4 -10x3 -24x2 -4x+4

Q: a) Show that the length of the arc of the curve y=f(x) where S(x) = Insecx 0SxS is 4 In(1+ v2)

A: We need to show that the length of the arc of the curve y=f(x) where f(x)=ln(sec(x)), 0≤x≤π4. The…

Q: By using Trapezoidal rule, the value of "h" in evaluating [(r' - 2x + 6)dx , by taking 10…

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Q: A. Use Simpson's rule to evaluate -dx ,by taking n= 4. Inx B. Find the length of the curve y = x…

A: Answer

Q: Using Simpson's One-Third Rule, an approximate value of 14 / V(x' + 3x)dx with 4 intervals, correct…

A: Given The given integral is ∫04x3+3xdx Simpson's one-third rule is ∫abfxdx=h3y0+yn+4y1+y3+y5+·  ·…

Q: a. y = cot¯(Ve") tanh(e") -1

A: Since you have asked multiple questions in single request so we will be answering only first…

Q: TE 4 To approximate cos(x) dx would Simpson's Rule, Midpoint Rule, or Trapezoidal Rule give a better…

A: We know ∫0π2cos(x)dx = 1

Q: Find the length L of the arc formed by y = In(sec x), 0 <x< n/6. CT/6 L= V1 + (f'(x))² dx where…

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Q: Use the Trapezium Rule with four strips to estimate the value of: dz. (In z)² Give your answer…

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Q: Find the value of dz, by Simpson's rd rule, using 8 subintervals, correct to 5x +7 four decimal…

A: Simpson's 13rd rule:∫ab f(x) dx = h3[(y0+yn) + 4(y1+y3+y5+….+yn-1)+2(y2+y4+y6+…..+yn-2)]

Q: Find the arc length of the catenary y = cosh x between x = 0and x = ln 2.

A: Given y=cosh(x)

Q: sketch, eva luate freverse integ ration order of 2. 2. 4-X 2y e dy dx 4

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Q: I Approximate "dn with accuracy l by te modified Trapozoidal Compo site rule.

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Q: Given tanh(x)+ tanh ¯' (y) = 1, show that, 1- y? 1 – x² dy dx

A: Formula,ddxtanh-1x=11-x2Note- Since multiple questions are asked, I am answering the first question…

Q: By using Trapezoidal rule, the value of “h" in evaluating (x² – 2x + 6)dx , by taking 10…

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Q: While evaluating approximate value of 7 | x² dx, using Trapezoidal rule, taking 4. n = 10, the value…

A: The given integral is ∫47x2 dx. Compare the above integral with its standard form ∫abfx dx and…

Q: Find the arc length of the graph of y = √(16 − x2) over the interval [0, 4].

A: Given: y=16-x2 interval [0, 4]

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Q: Find the length of the arc of the curve y = ln x over the interval: 1, 7| . Round the answer to four…

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Q: .A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

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Q: S arctan y dy y3

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Q: Use Gaussian Quadrature of order 5 to approximate 08 6 2 x-1 To how many decimal places is this…

A: Given that,    f(x)=∫286x-1dx                                  1 Using the Numerical Integral by…

Q: 1 Evaluate dx by using Trapezoidal rule. Hence obtain 1 + x2 he approximate value of .

A: I am attaching image so that you understand each and every step.

Q: 5. Find the length of the arc for x = 3 - Jy from y = 0 to y = 4

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Q: Use the Trapezoidal Rule with n = 4 to estimate f, (x³ + 1)dx.

A: We have to estimate ∫-11x3+1dx by using the Trapezoidal rule with n = 4.

Q: Use Simpson's Rule with n = 4 to estimate the arc length of the curve y = 0.5e-2x, 0 <x < 2. L = Só…

A: The curve, y=0.5e-2x, 0≤x≤2.

Q: The approximate value of dx by using Simpson's rule is 0.3480, then the error in the approximation…

A: Given Approximate value of the integral by Simpson's rule(Vs) = 0.3480 Now we will find the actual…

Q: Which one is the arc-length of the curve y =2V12x + 14, x E [12, 14]? 14 126x+219 dx 12 6x+7 14 18x2…

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Q: Given: y = arctan sinh find y' at x = 2 %3| cosh 1 %3D 1+sinh? 1 cosh 1 O y = %3D 1+sinh 1 cosh 1…

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Q: Determine the length of the arc x=ln y−(y^2)/8 for 1≤y≤2.

A: The solution are next step

Q: Find the arc length of y= x2/8 - ln(x) from x=1 to x=4

A: We find dy/dx of the given function.

Q: Find the value of a such that the arc length of the catenary y = cosh x for −a ≤ x ≤ a equals 10.

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Q: 2. For ' Arctan(xy) =y" find the value of k so that ky '=- at y = 4 4

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Q: Use the trapezium rule, with 4 strips, to estimate fe-a* dx on [0, 2]. What is the maximum error?…

A: Given integration is : ∫02e-x2dx The formula used in trapezium rule is :…

Q: Which one is the arc-length of the curve y =2/7x + 11, x E [7, 11]? 147x+280 dx 7x+ 11 14x2 +…

A: The curve y=27x+11 , x∈7,11

Q: Using Simpson's rule, what is the approximate value of ſ dx with n 10?

A: Given that, the integral is ∫0211+x3dx and the value of n=10. Note that, the Simpson's rule…

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: Approximate S“ In x dx using three rectangles of equal length and left end points. Is your estimate…

A: The given integral ∫1e2ln x dx, three rectangles and left end points.

Q: Use the Trapezoidal Rule with n = 4 to approximate the value of: +1)dx.

A: Given,  ∫12x3+1dx, n=4

Q: The tangent line to the graph of y = ecos x is parallel to y = 0 at Select one: Oa. x = 1/2 O b. x =…

A: We are authorized to solve only 1 question, please repost remaining questions Tangent line

Q: 3 Calculate the arc length of y = x? over the interval [1,5].

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Q: Differentiate y = e® – x² arctan x.

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Q: The approximate value of| dx by using Simpson's rule is 0.3639, then the error in the approximation…

A: Approximate value of ∫161x4dx by using Simpson's rule is 0.3639 To find the error in the…

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.