Estimate the minimum number of subintervals needed to approximate the integral dx with an error of magnitude less than 10-4 using Simpson's Rule.

Q: Use Simpson’s Rule with n=6 to estimate the area underthe curve  y= ex/x from x =1 to x= 4.

A: The given curve is y=exx from x=1 to x=4. We have to find an area of the curve by using Simpson's…

Q: Use the Trapezoidal Rule and Simpson's Rule with four subintervals to estimate x* dx.

A: Trapezoidal Rule

Q: Set up a definite integral for the length of the curve y = x3 over [1, 2]. Set up the integral and…

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Q: a. Find the derivative of ln (4q^7 – 10) dq. b. Using the result of the derivative above and the…

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Q: x sin (x²) cos(x²), from a = 0 to b = 3. Estimate the integral of the given function, using %3D…

A: The given function is fx=xsin3x2cosx2. Here, a=0, b=π2, and n=8. We have to approximate the integral…

Q: Use integration by parts to compute the integral S xsin(4x)dx and Inx dx

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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: Use the trapezoid rule with 4 intervals to approximate .2 am has 10 x dx Then compute the correct…

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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: Use five-segment trapezoidal rule to estimate the integral of the equation shown from a = 1 to b =…

A: Equation is f(x)=x2cos(x)The value of the table for x and y x 1 2 3 4 5 y 0.5403 -1.6646…

Q: use interval additivity to show that  (integral a to b)(x+1)^2 dx = F(b) - F(a)

A: Solving by interval addditive property we have

Q: Approximate the area under the curve y=x3 from x=0 to x=2 using a Right Endpoint approximation with…

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Q: 1. ntegral dx with 6 (x-4)2

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Q: Approximate the area under the curve Y=x3 from X=1 to X=4 using a Right Endpoint approximation with…

A: To find out the area under the curve using the right endpoint approximation with n=6

Q: Find the area under the curve y= 1/(4x+ 2) for 1 ≤ x ≤ 3. Give an exact answer.

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Q: Use Simpson’s Rule with n=4 to approximate the integral 8∫0√xdx.

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Q: Approximate the area under the curve y = x° from x = 3 to x = 5 using a Right Endpoint approximation…

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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.