a) Using Simpson's rule with the "n" number of strips to calculate approximate area under a curve as shown by the following definite integrals. Where "n" must be even and positive integer between 4 and 10. 1+ x2 b) Using the above definite integral to calculate the approximate area under a curve by Trapezoidal rule with the "n" number of strips where "n" must be even and positive integer between 4 and 10. c) Compare your result of part (a) and part (b) that which answer is more accurate? Justify your answer with by valid reason.

Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare…

A:

Q: Find the approximate area under the curve by dividing the intervals into n subintervals and then…

A:

Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = ex/7…

A:

Q: 2. Find the area of the region bounded by the following: y = sin x, y = tan x, x = 0, y = 1 2' (1i)…

A:

Q: 6. Use the Method of Midpoint Rectangles (do NOT use the integral or antiderivative) to approximate…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 1) Find the area under the function f(x)= over the interval 1<x<2. a) First sketch a graph of this…

A: To find the approximation of the area using mid point rule and actual error also in part b)

Q: 1. Does the definite integral [a,b]? Why or why not? 2. How would you calculate the total area of…

A: Here we have to use the concept of integration

Q: 16 – 22 Estimate the area under the graph of f(x) over the interval [ – 3, 4] using ten…

A:

Q: i) Approximate the integral x? sin x dx by Simpson's rule with n = 4. ii) Find the minimum n…

A: The Simpsons rule(1/3) is used to find the approximate value of a definite integral. Consider the…

Q: 1 over the interval (0, 2] using eight x + 1 Estimate the area under the graph of f(x) =…

A: We have to estimate the area under the graph of given function over the interval [0, 2] using 8…

Q: 10) An area is approximated to be 14 in using a left-endpoint rectangle approximation method. A…

A:

Q: a. Use the Trapezoidal Rule to approximate the integral. (Round your answer to four decimal places.)…

A: Step:-1 Trapezoidal Rule:-   ∫ab f(x) dx≈h2 fx0 +2 fx1+fx2+......+fxn-1+fxn Here, h=b-an and x0=a,…

Q: 3. SET UP the definite integral that will give the area of the shaded region (as shown below) using…

A: The solution are next

Q: 1 over the interval [3, 6] using ten Estimate the area under the graph of f(x) x + 2 approximating…

A:

Q: 1. Find the area of the region bounded by the given curves. Show the computed areas of sections…

A: Let's find.

Q: Find the area under the given curve over the indicated interval. (TYPE IN A WHOLE NUMBER, FRACTION,…

A: Using integration.

Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = 1/…

A: fx=1x to find the integral ∫1625fxdx=∫16251xdx to solve the integral proceed as follows…

Q: Use a definite integral to find the area under the curve between the given x-values.

A: f(x)=4x3,x1=1 to x2=2Area=∫x1x2f(x)dx      =∫12(4x3)dxApply the integral…

Q: Use the Errors in the Trapezoidal Rule and Simpson's Rule Theorem to estimate the errors in…

A:

Q: Estimate the area under the graph of f(x) : over the interval [2, 7] using ten approximating I + 4…

A: In the question we have to find the R and L

Q: Integrate the following definite integral to find the area beneath the curve using either the…

A: Given the definite integral   A=∫0π8(tan2x)2(sec22x)dx

Q: Find the area under the given curve over the indicated interval. (TYPE IN A WHOLE NUMBER, FRACTION,…

A: Solved below

Q: y = x* and y = x

A:

Q: Set up a definite integral that represents the area bounded by the graphs of the indicated equations…

A: Given: The functions y=16-x2, y=0, -4≤x≤4, To determine: The integrals which represents the area…

Q: (4) 6. Accurately sketch a graph of the region, shade the area in question, and use geometry to…

A:

Q: Given the curves y=(x^2)/2​  −4·x and y=−x^2+8,   Sketch both curves on the same coordinate plane…

A: Let's solve.

Q: Estimate the area under the graph of f(z) over the interval [3, 5] using four approximating…

A:

Q: 1. a). Find the area of the region bounded by the two lines y = x and y = 4 - x, and the y- axis…

A:

Q: Determine the area that is bounded by the following curve and the x-axis on the interval below.…

A:

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A:

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A:

Q: Find the area bounded by the graphs of the indicated equations. Compute answers to three decimal…

A:

Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare…

A:

Q: 11) Find the area of the region bounded by the curves y = 4x - x² + 4 and y = x. Sketch the area,…

A: The given functions are: y=4x-x2+4 and y=x Equate the right side of the equation to find the…

Q: 7. Use a definite integral to calculate the volume of a pyramid with square base of length 3 m and…

A: definite integral

Q: Use Simpson's Rule with n = 4 to estimate the area under the curve of y = In x from x = 2 to x = 6.…

A:

Q: Use (a) the Midpoint Rule and (b) Simpson’s Rule toapproximate the given integral with the specified…

A: Solution:- The given function is  f(x)=xcosxand limit is 0 to π  we have to calculate the above…

Q: Using the Trapezoidal Rule with = 4 subintervals approximate the area under the sine curve f (x) =…

A: Topic:- application of integration

Q: 1 over the interval 3, 7 using five approximating Estimate the area under the graph of f(x) x2 + 2…

A:

Q: Consider the graphs of f(x) = √√√x + cos x and g(x) = √√x + sin x over 13п the interval 0, . Answer…

A: Equate the expression of fx, gx and simplify to obtain the value of x.…

Q: ind the area bounded by x=4ay and a chord passing through its vertex. Show complete solution of…

A: Given curve is, x2=4ay The equation of the chord passing through its vertex is y=x The intersection…

Q: A hole of radius 3 is bored through the center of a sphere of radius 5. Let the cross-section of the…

A: Consider a cross section through the sphere, which we have centered on the origin of the origin of…

Q: Find the area enclosed by r=a (3-2cosØ). Show complete solution of points of intersection, your…

A:

Q: 1) Find the area under the function f(x) =→ over the interval 1<x<2. a) First sketch a graph of this…

A: Trapezoid Rule:      ∫abf(x)dx≃∆x2f(x1)+2fx2+2fx3+.........+2fxn-1+fxn

Q: 8. Find the area between the curves y = cos(x) and y =1 – cos(x) on the interval [–7, 7]. %3D

A:

Q: 1) Find the area under the function f(x) = over the interval 1<x<2. аге a) First sketch a graph of…

A:

Q: 1. Find the area of the region bounded by the given curves. Show the computed areas of sections…

A: Area bounded by the curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on…

Q: Find the area under the given curve over the indicated interval. (TYPE IN A WHOLE NUMBER, FRACTION,…

A:

Q: In finding the area underneath a curve, which among the Riemann sums and definite integral is the…

A: Riemann Sums : As we know that a Riemann sum is an approximation of a region's area, obtained by…

Q: 1. Find the area of the region bounded by the given curves. Show the computed areas of sections…

A:

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.