3 Estimate the minimum number of subintervals to approximate the value of V9x+4 dx with an error of magnitude less than 5x 10 * using a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for Simpson's Rule.

Q: Use the Midpoint Rule with the given value of  n toapproximate the integral. Round the answer to…

A: Width of each interval = (4-1)/6= 3/6=0.5  So the partition is 1, 1.5, 2, 2.5, 3 , 3.5 , 4 The…

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

A: Trapezoidal Rule

Q: Solve the area covered by the x-axis and f(x) = e^x from x= 1 to x = 4 with interval h = 0.25 using:…

A: ∫abf(x)dx≈Δx(f(x0+x12)+f(x1+x22)+f(x2+x32)+⋯+f(xn−2+xn−12)+f(xn−1+xn2)) Mid point rule and…

Q: Use the formula (JE-| / (true value)) * 100 to express |ET| as a percentage of the integral's true…

A: Mathematically the derivative of a function is defined as f'(t)=limh→0f(t+h)-f(t)h. According to the…

Q: The vahe of the integral fx*dx with step length 0.5 using Trapezoidal's nule is a) 0.375 b) 0.875 c)…

A:

Q: Use the Trapezoidal Rule to estimate the integral |dx using n = 4. What n is needed for 2 decimals…

A:

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

A:

Q: 3. Use the Trapezoidal and Simpson rule to approximate the value of x*dx, n= 6(use 4 decimal…

A: Given: ∫12x2 dx  We have to calculate the given interval by using Trapezoidal and Simpson rule with…

Q: Find the integral ∫y (square root of y+2) dy

A: To find: ∫ yy+2dy

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

A:

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: d) Find the volume of the solid formed when the area bounded by the curve y = 3x – x? and the lines…

A: The volume of the solid generated by the revolution of the area bounded by the curve y=f(x), x-axis…

Q: Use geometry to calculate (without integrating): o V16 – x2 dx Note that f (x) = v16 – x² is the top…

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

A: Solved below

Q: Use the 4_segment trapezoidal Rule to numerically integrate. S(0.2 + 25x + 3x²) dx

A:

Q: 5. Use the midpoint rule with n=5 to approximate Vx3 + 1 dx. Round to four decimal places.

A:

Q: Use the Midpoint Rule with n = 4 to approximate 2x the integral 1 dx to three decimal place.

A:

Q: Use the Midpoint Rule with the given value of  n toapproximate the integral. Round the answer to…

A:

Q: Use (a) the Trapezoidal Rule and (b) the Midpoint Rule with n=5 toapproximate the integral  integral…

A:

Q: 1. Find the area bounded by the curves y?=2ax, y?=4ax-a? 2. By integration, show that the area of a…

A: To find the area of the region bounded by given curves.

Q: 7. The integral used to find the length of the curve y=xbetween x = 0 and x = 4 is (Circle your…

A: I have Provided this answer in step-2.

Q: Show that if k is a positive constant, then the area between the x-axis and one arch of the curve y…

A: y = sin kx cuts the x axis at y=0. Solve for x.

Q: Use the Midpoint Rule with to approximate the givenintegral. Round your answers to six decimal…

A:

Q: The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate same number of…

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Q: The radius of a sphere is measured and found to be 3 ft. with a maximum error of 0.1 in. Find the…

A: The solution of the problem is given in the next step.

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

A: To Determine: Use the Trapezoidal Rule with n = 7  to approximate integral ∫020cosπxdx. Compare your…

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

A:

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

A:

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

A:

Q: (b) Suppose we wish to estimate the area 3 Vĩ dx 2 using the Trapezium rule.

A:

Q: 1 TIy. Suppose that the The volume of a right circular cone of radius x and height y is given by V =…

A: Given that the volume of a right circular cone of radius x and height y is given by V=13πx2y and the…

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

A:

Q: 23 Estimate I = (3x + 6x2)dx using midpoints and n 3 subintervals. %3D

A:

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: Find the indicated midpoint rule approximation to the following integral. S. -- dx using n= 8…

A: The limit for the integration is 1 to 2. So, the interval for the midpoint Riemann approximation is…

Q: The area enclosed between the curves p(x) = + *+ 3 and g(*) = O 16 is 18 49 O -49 O 9 36 O -16 O -36…

A: To find the area enclosed between the curves.

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(x) dx…

A:

Q: Estimate the value of the definite integral + 2) dx by using the Trapezoidal Rule. (Round your final…

A:

Q: 2. Consider the integral: (x4 – x³)dx and n = 4 | a) Find the midpoint estimate b) Find the…

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

A:

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral 2/3 | (3…

A:

Q: Use Simpson’s Rule with n = 10 to estimate the arclength of the curve. Compare your answer with the…

A: Given equation of the curve is y=x sin(x) ,      0≤x≤2π

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

A:

Q: Use the bisection method to find the root of equation f(x) = x2 - 2 in the interval [O, 4] with the…

A: The given function is fx=x2-2, and given interval is 0,4…

Q: Find the value of 'h' in 8 dx evaluating by 1+x Trapezoidal rule braking in 24 intervals. 1.25 0.25

A:

Q: 4. 29. Estimate the area under the graph in the figure by using (a) the Trapezoidal Rule, (b) the…

A: For (a), We will be finding the area by the trapezoidal rule.

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.