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 the tangent plane (linear approximation) to approximate the number (1.993 + 1.033)^1/2 . You…

A: Using the tangent plane (linear approximation) to approximate the number 1.993+1.03312.

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: n = 10, approximate the integral ST ₂ Give the error of approximation for each a cos rd.r

A: Mid point rule for integral .…

Q: Q1. For the function f(x) = 3x² + 5x – 1, determine the required average and instantaneous rates of…

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Q: The side of a square was measured to be 10cm with a possible error in measurement of 0.1cm. Use the…

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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: Write down an integral expressing the length of the curve y = cos x, 2 2

A: Apply the below formula: L=∫ab1+dydx2dx

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: e f² = ¹² Use Simpson's Rule to estimate dx with a maximum error of 0.1.

A: Simpson Rule According to Simpson's Rule, ∫abfxdx=∆x3fx0+4fx1+2fx2+........+4fxn-1+fx2

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: A company finds that the revenue R generated by spending x dollars on advertising is given by R =…

A: To find: The value of dRdx at x=1500. Given: The revenue generated function is R=1000+80x-0.02x2.…

Q: A mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the…

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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.