Compute for the area under the curve using integral calculus and trapezoid method.The area beneath the curve of the equation, is shown below. Write the C++ program that will compute for the area under the curve of the equation,f(x)=3x+x^2 Write the C++ program that will compute for the area under the curve of the equation,f(x) = 3x + x²Input:The lower limita.The upper limit b.The number of trapezoids.Compute for the area using trapezoids:Declare an array whose size will be equal to the number of trapezoids.Use a looping structure.Pass arguments to a module that will compute for the area of the trapezoid and return the areaback to the calling method.Each element in the array will be assigned the returned area for every trapezoid.Use an accumulator to compound the sum of each element in the array.Compute for the area using integral:Pass arguments to a module that will compute for the area under the curve and return the areaback to the calling method.Assign the returned area to a variable.Output:The area of each trapezoid.The area using the trapezoid method.The area using integral calculus.Percentage error (absolute).%Error =CINDOWS.Enter the value for aUse the screenshot below to guide you in completing the rest your logic.number of trapezoids:True value Experimental valueTrue valueunits squaredsredunits sedunited.units squared.units sed» using trapezoid ausing integral calculussquared.-x100uits squared.When you are ready to submit your work, use your own values for a, b, and the number of trapezoids.Please use realistic numbers to get a realistic result.Called a module and passed arguments to compute for the area of the trapezoid. The modulereturned the area back to the calling method.Called a module and passed arguments to compute for the area under the curve using integral. Themodule returned the area back to the calling method.Array size must be equal to the number of trapezoids.Used an accumulator variable to compound the areas stored in each array element.All answers are in 4 decimal places.2 Compute for the area under the curve using integral calculus and trapezoid method.The area beneath the curve of the equation, f(x) = x+3x²,x=0 to 00 is shown below.22283 2222° 9908070605040302010-10 1To solve the area using integral, the equation is as follows:*x+3x² dx00+³5+qTo solve the approximate area using trapezoid method, the equation is as follows:[+]Where,bis the upper limit.a is the lower limit.is the number or trapezoids or parts (more trapezoids will increase the accuracy).The equation to compute for the average length of a trapezoid:[f(x₁) + f(x+1)]The equation to compute for the width of the trapezoid:PTherefore, proving this equation was derived from the area of the trapezoid:a+b=·h

C++ code: #include<iostream> #include<iomanip> using namespace std; // Defining the…

Compute for the area under the curve using integral calculus and trapezoid method. The area beneath the curve of the equation, f(x) = x+3x²,x=0 to 00 is shown below. 22332222° 2 60 50 40 30 10 To solve the area using integral, the equation is as follows: *x+3x² dx +³+d To solve the approximate area using trapezoid method, the equation is as follows: [+] Where, is the upper limit is the lower limit. is the number or trapezoids or parts (more trapezoids will increase the accuracy). The equation to compute for the average length of a trapezoid: [f(x) + f(x+1) The equation to compute for the width of the trapezoid: 19 Therefore, proving this equation was derived from the area of the trapezoid: A=a+bh

Compute for the area under the curve using integral calculus and trapezoid method. The area beneath the curve of the equation, f(x) = x+3x²,x=0 to 00 is shown below. 22332222° 2 60 50 40 30 10 To solve the area using integral, the equation is as follows: *x+3x² dx +³+d To solve the approximate area using trapezoid method, the equation is as follows: [+] Where, is the upper limit is the lower limit. is the number or trapezoids or parts (more trapezoids will increase the accuracy). The equation to compute for the average length of a trapezoid: [f(x) + f(x+1) The equation to compute for the width of the trapezoid: 19 Therefore, proving this equation was derived from the area of the trapezoid: A=a+bh

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter14: Numerical Methods

Section: Chapter Questions

Problem 5PP

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