1 (a) Calculate the value of Jo dx correct to 3 significant figures taking six intervals by Trapezoidal Rule

Q: Sketch a graph of y = 8 on [- 5, 4] and use geometry to find the exact value of int -5 ^ 4 8 dx.

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

A: Area bounded by the curve .

Q: (d) Calculate the value of dx correct to 3 significant figures taking six intervals by Trapezoidal…

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Q: | Example 8.12. Use the Trapezoidal rule to estimate the integral exª dx taking the number 10…

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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: a. Find a curve with a positive derivative through the point (1,1) whose length integral is given…

A: The arc length of a curve is given by below integral that passes through the point (1, 1) and have…

Q: Estimate sinx? dx with an error of less than 0.001.

A: Given ∫01sin(x2)dx

Q: 53. Find the value of 1 dx using weddle’s rule. 1+x?

A: Weddle's law is a formula for solving numerical integration.

Q: Calculate the deriv L tan2tdt d_ dx II

A: Derivation of          is calculated as shown below

Q: The error is numerically computing the integral | 1 dx using the +4 trapezoidal rule with two…

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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: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

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Q: 3 dx by Simpson's rule breaking it into 6 intervals. Evaluate 2+x?

A: We have to evaluate the integral ∫2532+x2dx by Simpson's rule-breaking it into 6 intervals.

Q: Find the area bounded by the trigonometric curves 5ñ to - 4 3.667 square units 3.459 square units…

A: topic- area bounded by curves

Q: How do you use a Maclaurin serieis aproximation to estimate (Provided picture). Thanks!

A: First find the Maclaurin series for e^(x^2) using the Maclaurin series of e^xPlug x^2 in place of x.

Q: 4 1 -dx using the midpoint rule with three subdivisions to four decimal places. In(x) Approximate…

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to -1 (-24 x² – 10x³ -…

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

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

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Q: Find the mean value of over the interval [0,27] 4+ cosx

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

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Q: 8 Use right endpoints and 3 intervals to estimate S dx. 2

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Q: x = -sin 2y x = cos y --

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Q: Consider the intergral of (2x + 1) dx from 1 to 5 Estimate its value using 4 and 8 subdivisions of…

A: Note:- In given problem, you don't mention Simpson Rule name (Simpson 1/3 Rule or 3/8 Rule). Due to…

Q: 1. Use the trapezoidal rule with eight intervals to evaluate places. I = [dx 3 2 %3D correct to 3…

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Q: Use Simpson's rule with 3 8 intervals, to evaluate 2 dx, correct to 3 decimal places.

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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: Find all æ values on the graph of f(x) = 2x – 4 cos æ for 0 < a < 2n where the tangent line has…

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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: rea of the region between the sine curve

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

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Q: 16 Evaluate x*In 3x dx correct to three decimal places.

A: Given that, ∫12x2ln 3x To find- The value of the above integral. Concept Used- The above integral…

Q: In estimating cos(4x)dx using Trapezoidal and Simpson's rule with n - 10, we can estimate the error…

A: a = -1 b = 6 n = 10   h = (b-a)/10 = 0.7 h = 0.7   f(x) = cos(4x)   f'(x) = -4sin(4x) 0 = -4sin(4x)…

Q: Use Simpson's Rule with ne4 to estimate Cos"xdx COSTX ☺ For ☺ an upper bound for the estimate. Hint:…

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Q: Given that S." sin xdx = 2, find the average value of the sine function on the interval [0, π].…

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Q: Find all values 197. gh of aci on the the graph of f(x) = -3 sinxcosx where the tangent line is…

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Q: Find the definite integral 5 tan(x)dx using strips of width for the trapezium rule correct to three…

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Q: 7) Estimate the value of e dx using Simpson's rule using 8 subintervals.

A: Given: ∫02ex2dx Here, n = 8 subintervals

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

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Q: Š The minimum value of n required to approximate dx by composite Simpson's Rule with an error less…

A: Given integral is ∫02e−2xdx. We have to find the minimum value of n required to approximate…

Q: 8. Use Simpson's rule, with n = 8, to approximate fe sint dt. Compute the error if the true value

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Q: 1 Use either (3) or (8) in Section 8.6 to find upper bounds for the error in approximating dx by the…

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to x*+20x-126x + 2x +3 dx…

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Q: Compare the Trapezoidal rule and Simpson's rule approximations to x sin x dx and find a bound for…

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Q: How large should we take n in order to guarantee that the Trapezoidal Rule approximation for 6 5x*dx…

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Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +…

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Q: (b) Using the Trapezoidal rule with four strips (intervals), estimate the integral | sin (r/2) dr .…

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Q: The graph of f(x) = cos x and a tangent line to f through the origin are shown. Find the coordinates…

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Q: Given that ſ♫ sin xdx = 2, find the average value of the sine function on the interval [0, π]. Also,…

A: Please see the below picture for detailed solution .