How large should n be to guarantee that the Trapezoidal Rule approximation to 8 | (- 2* + 20z – 96z? + lx + 2)dx is accurate to within 0.01.

Q: Estimate the error in using the Trapezoidal Rule with n=8 when approximating the inetegral of…

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Q: (b) Find a value for n to ensure that the absolute error in approximating the integral xsin x dx by…

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral S7 n = 20…

A: we nee to find ∫π4π2ln(tanx)dx,  n=20 a=π4=0.7854,  b=π2=1.5708 ,  y=ln(tanx)…

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to x - 2x + 36x – 3x + 4)…

A: We have to find the value of n.

Q: (1) Use the trapezoidal rule and (2) Simpson's rule, with n= 10, to approxima te the integral. Round…

A: Topic : numerical methods

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to | (- - 62 + 24x2 – 2x…

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Q: 1- Use trapezium's Rule with n = 4 to approximate the integral Vx dx

A: We have to use formula of Trapezoid Rule.

Q: 3 Estimate the integral 1 dx by the trapezoidal rule using n = 4. + 1 Vx3

A: ∫abf(x)dx≈Δx(f(x0)+f(x1)2+f(x1)+f(x2)2+f(x2)+f(x3)2+⋯+ f(xn−1)+f(xn)2) where ∆x =b -an

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 203 – 96a? - lx - 2)…

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Q: How large should we take in order to guarantee that the Trapezoidaland Midpoint Rule approximations…

A: Given

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

Q: The approximated value of the integral fe* dx is equal to - Rule with step size (h=2). when using…

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Q: 5 2 +2 ) dx using Estimate I - n = 4 subintervals and (a) Left endpoints. (b) Right endnoints.

A: solution:-I=∫152x+2dx,     n=4f(x)=2x+2∆x=5-14=1(a) Left end pointI=∆xf(1)+f(2)+f(3)+f(4)…

Q: Solve the following problems on bond papers (maximum 3 bond papers) with 2 inch margin on all sides.…

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

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Q: Consider the integral Í dx . For which value of n the error in trapezoidal rule will be less than…

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Q: Use Simpson's rule with interval h = 1 to determine the approximate value of f V(1+ x3)dx. Give…

A: Given integral is ∫021+x3dx and h=1. We have to approximate the given integral by using Simpson's…

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

A: Solved below

Q: 2 1 The approximation of -dx by the composite Trapezoidal Rule with n=2 is O x+4 0.30833 0.40833…

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Q: How large should n be to guarantee that the Simpson's Rule approximation to dx is accurate to within…

A: Given:  ∫017ex2dx             where f(x)=7ex2 and a=0 , b=1.

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral…

A: Here the lower limit is π4 and upper limit is π2

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to | (- xª + 14x³ – 60x²…

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Q: Use the trapezoid rule with n = 70 to approximate | Væ4 + 1dx. You need to carefully write out -3…

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Q: Use the Trapezoidal Rule with n = 7  to approximate integral 0 to 20  sin (pie x) dx. Compare your…

A: The given function is fx=sinπx n=7

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: Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with…

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Q: 9-10 Use the Midpoint Rule with n = 4 to approximate the integral. 9. 2² dx

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

Q: In(2x + 2) · dx a) Use Trapezoidal rule with n=4 to approximate the integration b) Estimate the…

A: Given function is ∫04ln2x+2·dx   a) fx=ln2x+2 h=b-an=4-04=1 The function values are  x 0 1 2 3 4…

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 4x + 18x + 2x 3) dx is…

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Q: 3.) Determine the absolute and relative error that occurs when approximating the integral 32x² dx…

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Q: Using the trapezoidal rule with n = 4, estimate the integral / (x (x+1)² dx.

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Q: Use Simpson's rule with interval h = 1 to determine the approximate value of V(1 + x³ )dx. Give…

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Q: 4) Use the Trapezoid Rule and Simpson's Rule with n 6 to estimate Vx dx

A: Trapezoid Rule: ∫abf(x)dx=∆x2fx0+2fx1+2fx2+.........+2fxn-1+fxn                        where,…

Q: Compute the approximation  of the integral -4 to 4 e^(-x^2) using the trapezoid rule with n=4; you…

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Q: Find the indicated midpoint rule approximation to the following integral. 2 元 4 sin x dx using n = 6…

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Q: Approximate the integral S" x² sin x dx by Trapezoidal rule with n = 4. O Find the minimum n…

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Q: Use (a) the Trapezoidal Rule integral 1to 4    sin x dx                 with n= 5

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Q: Use Trapezoidal rule with 5 subintervals and 8 subintervals to find an approximation of x3V-2x4 +…

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to - 2 | (- x* – 12a –…

A: Given the given integral is ∫-4-2-x4-12x3-48x2+2x+5dx. Use formula for Trapezoidal rule…

Q: Use the Midpoint Rule with n = 4 to approximate the integral. 10 x² dx M4 =

A: The given integral is ∫210x2dx. The mid point rule states that if fxis continuous on [a,b][. Let n…

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 | (- x4 + 20x³ –…

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Q: 28. X (1+4x²)³ dx

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Q: Find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating the…

A: Given the integral: Hence we have

Q: The integral (16x² + 96x + 144)dx is approximated by the following left endpoint Riemann sum (each…

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Q: Q2 ) Use the Simpson's rule with (n = 4) to estimate thef²n sinx dx . 2

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Q: 39.) Show how to use (a) trapezoidal rule and (b) Simpsons rule with n=4 to 4 approximate ſ,"…

A: There are different methods of solving a definite integral without integrating it such as the…

Q: Find the length of the curve y = In x from x = V3 to a = 2/2. o 1+홀 In를 None of the choices. Please…

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Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h =, to approximate the integrale-2x²…

A: (a). Given integral is ∫13e-2x2dx. The step size is h=18. We know that the integral of a function fx…

Q: Use the Trapezoidal Rule withn=4 steps to estimate the integral. 3 16) dx Use Simpson's Rule with n…

A: 1.  According to the Trapezoid rule,…

Q: 3.a) Apply the Trapezoid and corrected trapezoid rule, with h =, to approximate the integral…

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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.