7 1. Approximate dx with six subdivisions to four decimal places using In x A. Midpoint rule B. Trapezoidal rule C. Simpson's Rule

Q: 1 (a) Calculate the value of Jo dx correct to 3 significant figures taking six intervals by…

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Q: Evaluate 112² (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

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Q: 2 Use the trapezoidal rule with n = 5 to approximate sin(x) -dx. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ,5…

A: Trapezoidal rule

Q: 23. Evaluate Jcxy dx + (x + y) dy along the curve y = x² from (-1, 1) to (2, 4).

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Q: correct to three decimal places by Trapezoidal rule with 1 +x dx Evaluate I= h=0-5.

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Q: 10 Use aepropriate substitution Ond then a trigonometric oubtitution to evaleiate the integial. dx…

A: This question can be solved using the concept of integration by substitution.

Q: 11. Determine the values of n and h required to approximate e2r sin 3x dx to within 10-4. Use a.…

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

Q: 4) a²y=+52y =14 yat (2,1) Find equátion of tangent?

A: Equation of tangent  y-y1=m(x-x1) (x1,y1)are the points at which equation of tangent is to be…

Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

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Q: 2. (a) Find the tangent line approximation to sin(x) near r 0. (b) Is the tangent line approximation…

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Q: 2 Approximate | sin(x²) dx with 12 subintervals by -4 (a) Trapezoidal rule. 1 rule. 3 (b) Simpson's…

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Q: (a) Determine the interval width so that the composite trapezoidal rule can be used to compute xe*dx…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: Evaluate 112x C: arc on y = x5/2 from (0, 0) to (4, 32) (2x - y) dx + (x + 3y) dy.

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Q: 1. Find the area under one arch of the curve y = cos- :cosex.

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Q: Find the indefinie intgrel wite 5 sec (2x) tan (2x) dx

A: Topic = Integration

Q: Evaluate S (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

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Q: Use trapezoidal with 3 level Romberg ( k=3) to evaluate 1 Пх - Пх* cos dx 4

A: The complete solutions are given below

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: 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: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: 10 Use Simpson's Rule with n = 8 to approximate f cosx dx. 2

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Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: Suppose L is the tangent line of f (x) = csc T at x = 2 . Where does L intersect the y-axis? Note:…

A: We have to find

Q: Use Simpson's rule with n = 6 to approximate %3D cos(a) dx 0.08 Keep at least 2 decimal places…

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x12 from (0, 0) to (4, 8) 528/5

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Q: The area under the entire curve is given by 00 dx. We have 3x-3 dx = lim 3x-3 dx -2 3x lim %3D -2 x…

A: the area under the  entire curve is given by ∫1∞3x3dx

Q: What is the area of the region between the sine curve and the x-axis from to 2 ? -1 2 1 4 3.

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: Ni cos(2?)a. Cos | x dx

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Q: 3 Estimate the error if S10 (Simpson's rule with n = 10) was used to calculate sin(4 x) dx .

A: I=∫03sin4xdx Integrating it- I=-cos4x403=-cos124+cos04=1-cos124=0.0054

Q: Estimate 1 7 cos(x2) dx 0 using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round…

A: I=∫017 cos (x2) dx             f(x)=7 cos (x2)b=1, a=0, n=4h=b-an=14=0.25aThe Trapezoidal…

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral SIn(tan x)…

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Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places…

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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: Grade: 107.5/156 Print Version dy sin(5æ) Find for y dx dy Preview ||

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Q: Page No. Date ry" - By + y =0; L dhe solutiom of Hhe differential uatio) Hhe idifferentialquation

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Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

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Q: Determine the length of the arc y=ln(cos x) for 0≤x≤π3.

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Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

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Q: Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x)…

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Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

Q: The length of one arch of the curve y = sin x is given by L = | VI + cos² x dx. 0, Estimate L by…

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Q: 1. Find by implicit defferentiation dy dx CS wanne+with CamScanne

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Q: 7 1 dx using the midpoint rule with four subdivisions to four decimal places. In(x) Approximate The…

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Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson's 3/8 rule with (n₂ = 3) to estimate tan-¹(2).…

A: We have to estimate the given function.

Q: The minimum value of n required to approximate xe dx by composite Trapezoidal rule with an error…

A: Find the minimum value of n required to approximate ∫02xe-xdx by composite Trapezoidal rule with and…

Q: 7 Show that: sech x dx = Sin¹ (tankx) + ( S note: * & Sim'u = dx 1-U² dx Cam multiply sechx by * you…

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