Derive the error estimates for the trapezoidal and Simpson’s rule? Using this find the error estimation of (question is in attached pic)

Q: 4. (a) In a complete sentence, tell why there needs to be an even number of subintervals in…

A: o find the solution of given statements

Q: Find the length of the segment of the curve y = (1/2) cosh 2x from x = 0 to x = In v5. Simplify your…

A: The length of the curve fx from x=a to x=b is defined by L=∫ab1+f'x2dx. Given fx=y=12cosh2x from x=0…

Q: A cylindrical can, open at the top, is to hold 400 cm3 of liquid. Find the height, h, and the…

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Q: Use the error bound for the trapezoidal rule to find the smallest N such that the error in…

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Q: 3 Estimate the minimum number of subintervals to approximate the value of| (4t° + 9t) dt with an…

A: Given: ∫034t3+9tdt To find: Minimum number of subintervals to approximate the integral value with…

Q: 2) By measurement, a triangle is found to have two sides of length 50 cm and 70 cm; the angle 1…

A: Follow the procedure given below.

Q: Trapezoidal method Quar x³dx for n=6 is equal to Blank 1 ("

A: Please refer to the image below

Q: The vertical distance covered by a rocket from 8 to 30 seconds is given by 30 140000 x = 2000 In…

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Q: Find the acute angle of intersection of the planes x = 0 and 6x – y+z – 9 = 0 to the nearest degree.…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the point P on the line y=2xthat is closest to the point (25,0). What is the least distance…

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Q: 5. The measurements of closed rectangular box are length, x = 5m, width y = 3m, and height, z =…

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Q: Consider the following rectangular piece of tinplate. An open-top cake tin is to be made by cutting…

A: Here, I am going to solve only 1st part for the remaining parts please post the question again and…

Q: chicles, bility that all the local tourist. vehiole

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Q: To determine the amount of water flowing down a certain 100-yard-wide river, engineers need to know…

A: Given :           The amount of water flowing down a certain 100 - yard wide river.…

Q: A Norman window is in the shape of a rectangle surmounted by a semi-circle. What is the ratio of the…

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Q: A water tank is shaped like an inverted cone with height 6 m and base radius 1.5 m. a. If the…

A: The work done is 66.13 × 103 J

Q: nive the newX value only of the ew Point after translating the ghlighted Point 2 Right. 4. -2 14 15…

A: Tanslating a point to right with 2 is simply adding 2 to that x coordinates.

Q: The measurements of closed rectangular box are length, x = 5m, width y = 3m, and height, z= 3.5m,…

A: In the question it is asked to calculate error in maximum possible volume and surface area

Q: In designing a spherical water tank, you are to use the formula for volume: (3R – h' V = nh? where V…

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Q: The trapezoidal rule and (ii) The Simpson's rule.

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Q: Who is correct? A figure on a coordinate plane is dilated by a scale factor that is less than one.…

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Q: ved in the approximation rapezoidal rule, the erro Simpson's rule, the error VOur answers accurate t

A: The function given is , fx=cos 4x , the integral has the limit a=-1, b=2 , and interval n=8. The…

Q: Find the exact value of . Find the error of approximation between the exact value and the value…

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Q: 2. A conical paper cup is to hold a fixed volume of water. Find the ratio of the height to base…

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Q: Use Trapezoidal Rule to approximate the given interval to the specified value of n. (Round 6 decimal…

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Q: A pair of similar cones have a scale factor of 3:5. What is the ratio of their surface areas? Please…

A: Ratio of surface areas is square of the scale factor.

Q: A)The Trapezoidal Rule with 3 equal length subintervals.  B)The Simpson’s Rule with 6 equal length…

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

Q: (b) The velocity of a particle which starts from rest is given by Table Q2 (b): (i) Examine the…

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Q: 6. Two vertical poles are 10 m apart. The poles are 5 m and 8 m high, respectively. They are to be…

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Q: Ld by using Evaluate 1+x2 (i) Trapezoidal rule, vie (üi) Simpson's 318 rule, (iv) Weddle's rule and…

A: Solving the above question using numerical integration method

Q: 32° А

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Q: The measurements of the diameters (in cms) of the plates prepared in a factory are given below.…

A: Given: The provided data is: Diameter 20-25 25-30 30-35 35-40 40-45 No. of plates 13 17 11 7 12…

Q: Use the Midpoint Rule, Trapezoidal Rule, and Simpson's Rule with ?=4 to estimate (the equation…

A: Consider the given problem: The objective is to solve the given problem.

Q: Consider the following rectangular piece of tinplate. An open-top cake tin is to be made by cutting…

A: This question is based on application of Derivatives.

Q: The largest interval for which the IVP : y' + Tm- = y(3) = 10 %3D %3D nigua rolution ir

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: A cylindrical can, open at the top, is to hold 700 cm³ of liquid. Find the height, h, and the…

A: Given that volume of the cylinder is 700 cm3 We have to find the height h and the radius r that…

Q: B- Use the Trapezoidal rule with n=2 to estimate dx, to find the absolute relative true error |E,?

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Q: 2 Estimate the minimum number of subintervals to approximate the value of 9. ds with an error of…

A: Given:       ∫129s2ds   a) Let f(s) = 9s2  If a=1, b=2  then f1s = -18s2  f2s=54s4  f3s=-216s5…

Q: Estimate the minimum number of subintervals to approximate the value of ds with an error of…

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Q: Gina dilates several line segments by different scale factors and observes their images. Afterward,…

A: The dilation of a line segment always result in the change of length by the absolute value of…

Q: Determine whether each of the following statements is true or false, and explain why Simpson’s rule…

A: Given statement is  Simpson’s rule usually gives a better approximation than the trapezoidal rule.

Q: What term describes the section between points A and D? line segment ray point Done → My Progress >…

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Q: Find the approximate value of + 1) d: using Trapezoidal Rule. Trapezoidal Rules a. Single…

A: Given that,  ∫abf(x) dx = ∫04x28+1 dx a) Trapezoidal rule for single application: ∫abf(x) dx = b-a2…

Q: The measurements of the diameters (in cms) of the plates prepared in a factory are given below.…

A: Skewness means lack of symmetry or the curve is not in the bell shape. There are two types of…

Q: A window frame must be built using exactly 12 metres of framing material. The window is in the shape…

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Q: The diameter of a circular disk is 30cm, with maxium error in measurement of 0.2cm. Use dierentials…

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Q: (b) Compare the actual errors in part (a) with the error estimates given by the Theorem about Error…

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Q: Given that a right circular cylinder is inscribed within a sphere, what is the least possible volume…

A: First we draw the figure as per the given information, Now, we will assume the following : Let,…

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.